Electrically small, range and angle-of-arrival rf sensor and estimation system

ABSTRACT

An RF emitter sensing device is provided comprising an antenna circuit and an estimator configured to output, for one or more incoming signals-of-interest (SoI), either or both of an estimated range to the emitter of each SoI, and estimates for one or more angles corresponding to the 3D angle-of-arrival (AoA) of each SoI, wherein: the antenna circuit has a plurality of ports that each output an output signal containing the one or more SoI, the antenna circuit including one or more multi-port antennas, each multi-port antenna having two or more ports, each multi-port antenna being configured to pick up a combination of one or more E-field signals and one or more H-field signals from each SoI, in a common volume of space.

FIELD OF THE INVENTION

The present invention relates to systems designed to detect and estimatethe angle of arrival (AoA) or direction of arrival (DoA) of propagatingwaves such as electromagnetic waves and also characterize theirpolarization and also estimate the range to the emitter of a wave.Systems that provide both AoA and range estimation are commonly calledpassive geolocation systems. AoA estimation systems are also commonlyreferred to as direction finding (DF) systems. More specifically thepresent invention relates to an RF emitter sensing system that includesin its antenna system what is known in the literature as a {right arrowover (p)} cross {right arrow over (m)} antenna (PxMA) element, and inparticular, PxMA embodiments that maintain high front-to-back ratio(i.e. high directivity) to arbitrarily low frequency. More specificallythe present invention relates to an RF emitter sensing system thatprocesses the signals from the antenna system that includes a highdirectivity at arbitrarily low frequency PxMA to (1) enable self E-fieldand H-field sensitivity calibration, (2) mitigate self noise, (3)mitigate homogeneous environmental noise, (4) mitigate multipath such asfrom sky-wave versus ground-wave paths, and (5) enable accurate AoA andpolarization characterization of signals so weak that they are below thenoise floor of, and cannot be received by, a standard receiver intendedto receive and demodulate the signal of interest, and (6) enableaccurate estimation of the range to the emitter.

BACKGROUND OF THE INVENTION

A key problem of current DF systems is their large size, weight, powerconsumption, and setup time, when they must operate at low frequencies,such as a less than a few MHz. For many years, the government hasadvertised requests for proposals to solve this problem. Many journalarticles from radio operators to government researchers to universityprofessors, have been written attempting to solve this problem. What isdesired is an RF emitter sensing device that operates at low frequenciesand particularly at less than a few MHz, that is also small enough to behandheld or man wearable (e.g. contained within a backpack or in anoperators clothing), or small and light enough to fly on a miniatureunmanned aerial vehicle (UAV). The disclosed RF emitter sensing deviceis a solution to this long-standing problem. The disclosed RF emittersensing system includes (a) antennas that are unique in that they areextremely wide bandwidth and their directivity (i.e. front-to-backratio) improves as the frequency goes down, allowing the DF system tooperate to arbitrarily low frequency regardless of how small it is, and(b) signal processing methods to enhance its sensitivity and accuracy tohelp mitigate the fact that the energy collection area of the miniatureantennas is small. The small high directivity antennas and the signalprocessing methods, taken together, create the long asked for DF system.

The angle-of-arrival (AoA) or direction-of-arrival (DoA) of a signal ofinterest (SoI), along with range and polarization, can be expressed in aspherical coordinate system, such as pictured in FIG. 15. Standardgeometric rotation and translation calculations can be used to change onobject's pose (position and orientation) within a coordinate system orto convert a pose between coordinate systems. In this document we willuse the term AoA to mean either a single angle, such as azimuth, or thecombination of angles, such as azimuth and elevation, in a definedcoordinate system.

For example, in an earth-centric 2D planer coordinate system with theplane parallel to a point on the earth's surface, AoA typically means anazimuth angle, or in other words, a compass direction. The plane couldbe pictured as the x-y plane in FIG. 15. Azimuth is sometimes measuredas a counter-clockwise angle from east where 0 degrees means due east,90 degrees means due north, and the angular range covers from 0 to 360degrees. With this azimuth angle definition, in FIG. 15, there would beno z-axis since it is a 2D coordinate system, the x-axis would aim dueeast, the y-axis would aim due north, and φ would be the azimuth angle.

For another example, in an earth-centric 3D coordinate system, AoAtypically means a combination of angles, an azimuth-angle and anelevation-angle. The elevation-angle is typically understood to be anangle covering −90 to 90 degrees relative to a plane parallel to thesurface of the earth, where 90 degrees means straight up from theearth's surface toward outer space, −90 degrees means straight downtoward the center of the earth, and 0-degrees means parallel to theearth's surface. Given this elevation angle definition, in FIG. 15, 90−θdegrees would be the elevation angle.

Depending on the application, the desired output of the RF emittersensing system may be either 2D or 3D. Typically, different applicationshave different lists of desired outputs that also include items such asthe SoI's polarization, frequency, magnitude, duty-cycle,peak-to-average ratio, repetition rate, modulation type, event time andthe confidence level of these estimates. A confidence level is astatement such as 95% of the estimates will have an error of less than agiven amount like, for example, 1 degree, or 10 Hz, or 2 dB, etc.

REFERENCES

The following references are incorporated by reference in theirentirety.

-   Reference 1: Introduction into Theory of Direction Finding,    2011-2012 Rhode Schwarz catalog Radiomonitoring & Radiolocation.-   Reference 2: Paul Denisowski, A comparison of radio    direction-finding technologies, Rohde & Schwarz.-   Reference 3: R&S ADDx Multichannel DF Antennas Product Overview,    Version 4.00, September 2013.-   Reference 4: W. Read, Review of Conventional Tactical Radio    Direction Finding Systems, Communications Electroinic Warfare    Section, Electronic Warfare Division, Defence Research Establishment    Ottawa, Technical Note 89-12, May 1989.-   Reference 5: Sathish Chandran, Editor, Advances in    Direction-of-Arrival Estimation, Artech House 2006, Norwood Mass.    ISBN-10: 1-59693-004-7.-   Reference 6. Lan-Mei Wang, Gui-Bao Wang, Cao Zeng, “MUTUAL COUPLING    CALIBRATION FOR ELECTRO-MAGNETIC VECTOR SENSOR.” Progress In    Electromagnetics Research B, Vol. 52, pp 347-362, 2013.-   Reference 7: Oger M., Marie F., Lemur D., Le Bouter G., Erhel Y.,    Bertel L., “A method to calibrate HF receiving antenna arrays.” IEE    Ionospheric Radio Techniques Symposium, London: United Kingdom    (2006).-   Reference 8: Cecconi, B., and P. Zarka (2005), “Direction finding    and antenna calibration through analytical inversion of radio    measurements performed using a system of two or three electric    dipole antennas on a three-axis stabilized spacecraft.” Radio Sci.,    40, RS3003, doi:10.1029/2004RS003070.-   Reference 9: Baum, C. E., “Some Characteristics of Electric and    Magnetic Dipole Antennas for Radiating Transient Pulses.” AFWL    Sensors and Simulation Notes 125 (January 1971).-   Reference 10: J. S. Yu, C-L James Chen, and C. E. Baum, “Multipole    Radiations: Formulation and Evaluation for Small EMP Simulators.”    Sensor and Simulation Notes 243 (July 1978).-   Reference 11: E. G. Farr and J. Hofstra, “An Incident Field Sensor    for EMP Measurements.” Electromagnetic Compatibility, IEEE Trans.    on, May 1991, 105-13, Also published as Sensor and Simulation Notes    319 (July 1989).-   Reference 12: Baum C. E., “General properties of antennas.”    Electromagnetic Compatibility, IEEE Transactions on, vol. 44, no. 1,    pp. 18-24, February 2002 doi: 10.1109/15.990707. Also Sensor and    Simulation Notes 330 (July 1991);-   Reference 13: F. M. Tesche, “The PxM Antenna and Applications to    Radiated Field Testing of Electrical Systems, Part 1, Theory and    Numerical Simulations.” Sensor and Simulation Notes 407 (July 1997).-   Reference 14: F. M. Tesche, T. Karlsson, and S. Garmland, “The PxM    Antenna and Applications to Radiated Field Testing of Electrical    Systems, Part 2, Experimental Considerations.” Sensor and Simulation    Notes 409 (July 1997).-   Reference 15: E. G. Farr, C. E. Baum, W. D. Prather, and T. Tran, “A    Two-Channel Balanced-Dipole Antenna (BDA) With Reversible Antenna    Pattern Operating at 50 Ohms” Sensor and Simulation Notes 441    (December 1999).-   Reference 16: McLean, J., H. Foltz, and R. Sutton. “Conditions for    Direction-Independent Distortion in UWB Antennas.” Antennas and    Propagation, IEEE Transactions on 54, no. 11 (November 2006):    3178-83. doi:10.1109/TAP.2006.883956.-   Reference 17: Mayes, P. E., W. Warren, and F. Wiesenmeyer. “The    Monopole Slot: A Small Broad-Band Unidirectional Antenna.” Antennas    and Propagation, IEEE Transactions on 20, no. 4 (July 1972): 489-93.    doi:10.1109/TAP.1972.1140250.-   Reference 18. McLean, J., and R. Sutton. “Practical Realization of    PxM Antennas for High-Power, Broadband Applications.” In    Ultra-Wideband, Short-Pulse Electromagnetics 7, Chapter 30, edited    by Frank Sabath, Eric L. Mokole, Uwe Schenk, and Daniel Nitsch,    267-75. Springer New York, 2007.-   Reference 19: McLean, J. S., and G. E. Crook. Broadband Antenna    Incorporating Both Electric and Magnetic Dipole Radiators, U.S. Pat.    No. 6,329,955.-   Reference 20. McLean, J. S. PxM Antenna with Improved Radiation    Characteristics over a Broad Frequency Range. U.S. Pat. No.    7,388,550 Jun. 17, 2008.-   Reference 21: G. F. Brown, Direction finding antenna U.S. Pat. No.    8,179,328, 15-May-2012.-   Reference 22: Schroeder, K., and K. Soo Hoo. “Electrically Small    Complementary Pair (ESCP) with Interelement Coupling.” Antennas and    Propagation, IEEE Transactions on 24, no. 4 (July 1976): 411-18.    doi:10.1109/TAP.1976.1141376.-   Reference 23: Mayes, P. E. Stripline Fed Hybrid Slot Antenna, U.S.    Pat. No. 4,443,802 April 1984.

Direction Finding Background

Reference 1 and Reference 2 are easy to read introductions into thetheory of direction finding that discuss and compare various techniquesused to implement DF systems. Reference 3 gives an overview of differentantenna systems used in DF systems. Reference 4 and Reference 5 providein-depth treatments of direction finding techniques. A tremendous amountof effort has gone into calibrating or mitigating errors in DF systems.Reference 5, Reference 6, Reference 7, and Reference 8 provide in-depthbackground on error mitigation and calibration techniques. Reference 9through Reference 16 provide detailed theoretical and practicalbackground into a {right arrow over (p)} cross {right arrow over (m)}antenna element, which we will call a “PxMA” element. The practicalrealizations shown in Reference 11 and Reference 15 show the operationof a PxMA embodiment that operates to an arbitrarily low frequency, asopposed to antennas such as those shown in Reference 17 throughReference 23, which include multiple elements, such as loops anddipoles/monopoles or slots and dipole/monopoles, multiple slots, ormultiple dipole/monopoles and have PxMA characteristics over a passbandthat does not extend to an arbitrarily low frequency.

To find the source of RF emissions, it is desirable to have a small, manportable, RF emitter sensing system. There are many uses for RF emittersensing systems. They can be used to track or find objects that have anRF transmitter, like an emergency beacon, or animals whose daily habitsor migratory habits are being studied. As the use of wireless devicesfor remote sensing, remote control, voice and data communication, and aplethora of applications has expanded, as well as the use of digitaldevices that radiate unintentionally, the likelihood of improperlyradiating RF energy at levels beyond regulatory standards has likewiseexpanded. Equipment operating at levels beyond regulatory standards cancause harmful interference. Often, the source and location of theimproper emissions is unknown. RF emitter sensing systems are used tofind the aberrant transmitter.

Victim systems to an aberrant transmitter can have a largeantenna-system such as a large antenna, or a large array of antennas,that can collect significant energy even from small signals. This factgives them high sensitivity, causing them to be disturbed by smallaberrant signals. On the contrary, a portable DF system must have asmall antenna or antenna-system; otherwise, it is not portable. As such,it cannot collect as much energy as the large antenna-system. Not onlyis the sensor smaller, but the location of the sensor is often poor. Forexample, the victim system might be strategically located near the topof a tall tower or building. In contrast, to maintain easy and covertportability the DF antenna may be only waist or head high. Thus, it willbe appreciated that a method for obtaining a high signal to noise ratio,even with a small poorly located antenna-system, is needed for a manportable DF system.

Another difficulty in realizing an effective RF emitter sensing systemis that propagating waves reflect off of and diffract around randomobjects like mountains, buildings, the ground, rocks, cars, trucks,people, etc. and also refract off of the ionosphere. In contrast, wavesfrom objects and nearby reflections that are far away relative to thesize of the RF emitter sensing system's antenna array are seen asessentially plane waves, the waves from nearby sources can often be muchmore spherical when the RF emitter sensing system's antenna array isrelatively large. A plane wave collected by an array produces a distinctpattern of amplitudes and phases at the ports of the antenna system,allowing the direction of the plane wave to be estimated. But aspherical wave from an unknown direction and with an unknown radiustypically produces a pattern of amplitudes and phases at the ports thatcan be confusing and does not match a plane wave. Thus, it will beappreciated that a method is needed that can estimate the AoA with avery small array so that even close-by signals still appear planarenough to give accurate AoA estimates.

Another difficulty in realizing an effective DF system, especially aportable one, is the tight mechanical and electrical tolerances requiredacross a plethora of interconnected items that must all work together inorder for a DF system to perform its function. Many DF systems are basedon using a loop (sometimes made as a slot) antenna for a magnetic(H-field) sensor and a dipole or monopole antenna for a electric field(E-field) sensor. Assuming their relative position is known andrelatively close together, such as less than ½ wavelength apart, theoutputs of these antennas can be adjusted in magnitude and phase andthen summed so as to create a cardioid pattern in a passband that isuseful for direction finding. The problem is that these loop/dipolecombinations do not work (i.e., provide high directivity) to anarbitrarily low frequency. The sensitivities of the different elementsto the E and H field components of the incident electromagnetic (EM)field must be extremely well matched in order to produce a reasonablecardioid pattern (i.e., one with a back to front ratio of −15 dB orbetter) so that AoA estimation can be done accurately.

This sensitivity-matching is problematic because the loop antenna andthe dipole antenna don't inherently share the same sensitivity,impedance, frequency response, or impedance versus frequency. Moreover,while broad-banding approaches may be used, these antenna elements aswell as their matching networks are resonant and thus narrowbanddevices. Beyond these differences, when the elements are separatelymatched and amplified, the signal chain for the loop antenna and thedipole antenna must match and be stable across all frequencies. Thesignal chain components include impedance-matching circuits,transmission line lengths, and gains/losses and delays in amplifiers,mixers, switches, filters, etc. that make up the multiple signal paths.To end up with a cardioid pattern requires all these to match at allfrequencies of interest. The inability to maintain tight mechanical andelectrical tolerances causes reduced reliability and higher AoAestimation errors. Steps taken to improve or mitigate sensitivity tothese tolerance issues typically require offline calibrationmeasurements and cause increased expense, complexity, size, weight, andpower use. In light of these difficulties, it will be appreciated that aDF system is needed that that is inherently broadband at lowfrequencies, inherently calibrated, and can not only estimate the AoAusing one or more small EM sensor elements, but is also non-resonant,enabling it to accurately capture the waveform shape to aid in itsidentification or characterization.

While the above paragraph speaks to the problems for a single vectorfield sensor, when an array of these sensors are used, the matching mustextend across multiple vector sensors. Thus, it will be appreciated thatit would be advantageous for the RF emitter sensing system to use avector field sensor that has an extremely repeatable cardioid pattern,transient response, and sensitivity across multiple units. In otherwords, the sensor should be highly immune to mechanical and electricaltolerances.

Another difficulty is that there is need for the man portable DF systemto operate at low frequencies, yet at broad bandwidths. While a tuningnetwork can be employed, it must be set for one center-frequency at atime, providing only one narrow band of operation at a time. Use oftuning networks also slows reaction time and adds weight, cost,complexity, and a controller to manage its settings. Thus it will beappreciated that a method for obtaining wideband operation withouttuning, including down to arbitrarily low-frequency, is highlydesirable.

At higher frequencies, wideband antennas such as spirals, log periodic,and Vivaldi antennas are sometimes used. But these antennas introduce abeam pattern (including magnitude, polarization, and group delay as afunction of angle) whose magnitude and polarization is not symmetricabout the main axis. Furthermore, the non symmetry varies from unit tounit since it is sensitive not only to mechanical tolerances, but alsoto the electrical tolerances of the matching networks (such as aquadrature-hybrid's magnitude and phase balance). All thesenon-symmetric factors are important, especially for a fully polarimetricDF systems. These non-symmetries limit the system's accuracy not only inestimating the AoA, but also with respect to the polarization andtime/frequency properties of the waveform. Thus it will be appreciatedthat a method for obtaining a symmetric beam pattern that is insensitiveto tolerances and matching networks is needed.

Another difficulty is that man portable RF emitter sensing systems arerepeatedly assembled, disassembled, carried around, packed and unpacked.This man-handling makes it all the more difficult to maintain tighttolerances. In practice, even though a RF emitter sensing system mightbe made to work in a lab environment, the harsh environment of a manportable system can cause RF emitter sensing systems to give un-reliableresults, or to simply stop functioning altogether.

It would therefore be desirable to have, and is the object of theinvention to construct, a small man-portable DF system thatsimultaneously (1) allows and has electrically small antenna elementswith the ability to operate at arbitrarily low frequency, (2) has highsensitivity even though the antennas are electrically small, (3) issmall, light-weight, low-power and low-cost (4) has disassembly andassembly times, and set-up tolerances, that are easy to maintain in aharsh, man-portable environment, (5) provides accurate AoA,polarization, and range estimates, and (6) provides the accurate AoA,polarization, and range estimates quickly.

SUMMARY OF INVENTION

The invention discloses the use of one or more PxMA elements in an RFemitter sensing system that estimates one or more of, the direction ofarrival, the polarization, and the range, to an emitter, where the PxMAelement maintains high directivity (i.e. high front-to-back ratio) toarbitrarily low frequencies and where the PxMA element is comprised ofone or more pairs of conductive surfaces offset from one anothercomprised of a first conductive surface and a second conductive surfacewith one or more pairs of ports, or port-pairs, wherein each port-pairhas a first port and a second port, and wherein each port is formed by aconnection to the two conductive surfaces, and wherein each port-pairforms a loop going from the first terminal of said first port, throughsaid first conductive surface to the first terminal of said second port,through said second port to the second terminal of said second port, andthrough said second conductive surface to the second terminal of saidfirst port, and through the first port back to the first terminal of thefirst port to complete the loop. In some embodiments, when there is botha first port-pair and a second port-pair connected to a pair ofconductive surfaces, a construction line going between said firstport-pair and a construction line going through said second port pairare preferred to be at 90 degrees to each other. When a pair ofconductive surfaces has two pairs of ports, it is called a QPA forquad-port-antenna. When a pair of conductive surfaces has one pair ofports, it is called a DPA for dual-port-antenna. When three pairs ofconductive surfaces are centered on a common center point to occupy acommon volume of space, and each conductive surface pair attaches to oneport pair, the antenna is called an HPA for hex port antenna. When threepairs of conductive surfaces are centered on a common center point tooccupy a common volume of space, and each conductive surface pairattaches to two port pairs, the antenna is called a DHPA for dual hexport antenna or 12-PA for 12-port-antenna.

FIG. 3 illustrates a DPA where the conductive surfaces are 305 and 310and the port-pair is on opposite edges of the conductive surfaces. FIG.4 illustrates a DPA where the pair of conductive surfaces are 305 and460 and the port-pair is on opposite edges of conductive surface 305,and conductive surface 460 is larger than conductive surface 305 suchthat conductive surface 460 can be thought of as a ground plane that maybe place on the ground or some large object such as an aircraft wing orroof top. As opposed to the surfaces bending less than 90 degreesextending outward to make the port connection points farther apart, thesurfaces can also be bent greater than 90 degrees to make the portconnections closer together than the extent of the conductive surfaces.Similarly, the conductive surfaces can have a protrusion to establishthe connection to a port, also allowing the extent of the surface toextend past the port positions. FIG. 5 illustrates a DPA where theconductive surfaces 505 and 510 wrap around a cylinder and the port-pairis on opposite edges of both conductive surfaces. This shape flexibilityallows the antenna to be optimized for various load impedances and tofit in the space needed by different applications.

The invention also discloses a QPA having four ports and comprised of apair of DPAs that share the same volume of space and the same conductivesurfaces. FIG. 6 is a mechanical drawing of a QPA. It shows a pair ofPxMA elements that share a common pair of conductive surfaces 605 and610, where one pair of ports, or port-pair, is oriented orthogonally tothe other port-pair. One DPA uses a port-pair comprised of port-1 andport-2 in FIG. 6. The other DPA uses a port-pair comprised of port-3 andport-4 in FIG. 6. FIG. 7 is a mechanical drawing of another QPAembodiment where a pair of DPAs share a common pair of conductivesurfaces 705 and 710, where one port-pair is oriented orthogonally tothe other port-pair. One DPA uses the port-pair comprised of port-1 andport-2 in FIG. 7. The other DPA uses the port-pair comprised of port-3and port-4 in FIG. 7. The QPA has the same shape flexibility as the DPA,allowing the antenna to be optimized for various load impedances and tofit in the space needed by different applications.7

The invention also discloses a hex or six (6) port PxMA antenna (HPA)and a twelve (12) port or dual hex-port PxMA antenna (DHPA) that operateto arbitrarily low frequency, and its use in a DF system. These areuseful for a minimum size 3D and fully polarimetric RF emitter sensingdevice embodiments. Rather than using three DPAs or three QPAs that areoriented orthogonally to each other, an embodiment can use a single HPAor DHPA, which allows three DPAs or QPAs to share the same volume. Inother words, all six HPA ports or all twelve DHPA ports share the samespace. The spatially merged antenna allows tighter manufacturingtolerances on keeping the twelve ports orthogonal, tighter mutualcalibration, and a smaller total volume to support six orthogonal ports,or twelve ports. FIG. 19B, is a mechanical drawing showing the DHPAconfiguration, while FIG. 19A shows an HPA configuration. FIG. 19B showsthree pairs of conductive surfaces, a first pair 1 a and 1 b having twopairs of ports, a second pair of conductive surfaces 2 a and 2 b havingtwo pairs of ports, and a third pair of conductive surfaces 3 a and 3 bhaving two pairs of ports. The HPA in FIG. 19A is a subset with one setof ports removed such that only one pair of ports for each pair ofconductive surfaces remain. The conductive surfaces in FIGS. 19A and 19Bare shown with a flat and square main body on the faces of a cube. Butthese surfaces can take on other shapes such as being circular insteadof square, or being non-flat (such as forming the shape of a sphereinstead of a cube). Similarly, part of the conductive surfaces appear asthin wires that connect the main body of the conductive surfaces to thefeed points, but the conductive surface can be shaped such that theseconnections have other shapes, such as being triangular tapers with thesame shape flexibility as a DPA or QPA. In addition to obtaining asmaller total volume, the spatially merged antenna (1) operates betterin a multipath environment since all six EM fields are measured in theexact same location, (2) allows tighter manufacturing tolerances forkeeping the ports fixed relative to each other (e.g. orthogonal), and(3) achieves tighter mutual calibration. In any embodiment wheresurfaces have more than one port-pair (e.g. QPA, HPA, DHPA), the surfacemay be split into a pair of slightly offset surfaces so that eachport-pair connects to a separate surface. In all cases (DPA, QPA, HPA,DHPA) there is also flexibility to place slits or slit patterns in theconductive surfaces to force currents to flow in preferred directionsand at preferred frequencies if desired. Frequency selective surfacesmay be used to operate at preferred frequencies, and be relativelyinvisible or reflective at other frequencies.

Multi-port antennas can be conceptually cut in half, where port-pairsare split between the two halves, such that the first-half of themultiport antenna is the half of the antenna that the signal arrives atfirst, and the other-half is the half that the signal arrives at afterit passes the first half. In this case, the ports in the first halfoutput a signal that is proportional to the sum of the magnitude of theE and H fields since the E and H fields have the same sign. The ports inthe other half output a signal that is proportional to the differencebetween the magnitude of the E and H fields since the E and H fieldshave opposite signs. If the antenna's sensitivity to the E and H fieldsare matched, both the sum and the difference output voltages havecardiod patterns but the cardiod patterns point in opposite directions.This sum and difference operation is shown pictorially in FIG. 11.

As shown in FIG. 1A, the invention discloses an RF-emitter sensingdevice including an antenna circuit and an estimator configured tooutput, for one or more incoming signals-of-interest (SoI), one or moreof (a) an estimated range to the emitter of each SoI, (b) estimates forone or more angles corresponding to the 3D angle-of-arrival (AoA) ofeach SoI, and (c) an estimated polarization of each SoI.

In this case, the antenna circuit has a plurality of ports that eachoutput an output signal containing the one or more SoI. The antennacircuit includes one or more multi-port antennas. Each multi-portantenna has two or more ports. Each multi-port antenna is configured topick up a combination of one or more vectors of the E-field signal andone or more vectors of the H-field signal from each SoI, from a commonvolume of space, or in other words, the same or identical volume ofspace. The estimator element is configured to output, for each SoI, oneor more of (a) an estimated range, (b) an estimated AoA, and (c) anestimated polarization. It estimates one or more angles corresponding tothe AoA of each SoI by receiving the output signals from the antennacircuit, and generating one or more of an estimated range to the emitterof each SoI, and estimates for one or more angles corresponding to theAoA of each SoI and an estimated polarization. The multi-port antenna isconfigured such that the one or more E-field signals and the one or moreH-field signals can be isolated from each other by combining the outputsignals from the various ports. Each multi-port antenna can also beconfigured such that each port has a nominally cardioid beam pattern inall planes containing a common axis of symmetry about the cardioid beampattern. Nearly ideal cardioid beam patterns are generated by adding andsubtracting weighted versions of the isolated E-field and H-fieldsignals.

If needed in particular applications, the estimator may also beconfigured to isolate particular signals of interest from otherextraneous signals and noise. FIG. 1B is a block diagram similar to FIG.1A but that explicitly shows an isolator element.

In some applications, the isolator function can be configured at thetime of manufacturing to address well known signals in the intendedapplication. In other applications it is advantageous to allow a user tospecify parameters that identify one set of characteristics thatrepresent the desired signal and another set of characteristics thatrepresent interference that should be rejected. Similarly, in someapplications, the estimator can be configured to output specific itemssuch as AoA or range or polarization outputs. In other applications itis advantageous to allow a user to define the items they want the systemto output. To address this variety of needs, FIG. 1A and FIG. 1B show auser input path that sometimes may not be used, but other times may beused for defining parameters for a set of one or more SoI, or may beused to define a set of outputs needed, or may be used to define systemstates or configurations such as power-on, power-off, sleep, idle, etc.or orientations and locations of different ports in the antenna circuit,or the orientation of the system relative to something else, such as theorientation relative to the earth, or the orientation relative to thevehicle carrying the DF system.

As shown in FIG. 1B, a DF system is disclosed for determining the AoA,polarization, and range to the emitter of a signal that:

-   -   (1) contains or receives user data that includes items such        as: (a) SoI-isolation-metrics that can be used to isolate the        SoI, such as one or more of: the center frequency, bandwidth,        modulation characteristics, occurrence timing, polarization,        field strength, stability of field strength, constraints on the        range of potential angles of arrival, and known multipath        geometries; (b) a list specifying one or more desired        outputs; (c) the antenna-system's port configuration; and (d)        the time and date and pose (position and orientation, e.g., x-,        y-, z-position and roll, pitch, yaw orientation) of a reference        position on the DF system relative to an earth coordinate        system; and    -   (2) is comprised of:    -   (a) an antenna-system 101, with an output for each antenna        element port, and which includes one or more PxMA elements where        the PxMA element is a pair of conductive surfaces offset from        one another comprised of a first conductive surface and a second        conductive surface with one or more pairs of ports, or        port-pairs, wherein each port-pair has a first port and a second        port, and wherein each port is formed by a connection to the two        conductive surfaces, and wherein each port-pair forms a loop        going from the first terminal of the first port, through the        first conductive surface to the first terminal of the second        port, through the second port to the second terminal of the        second port, and through the second conductive surface to the        second terminal of the first port, and through the first port        back to the first terminal of the first port to complete the        loop, and wherein when there is both a first port-pair and a        second port-pair, the port-pairs are orthogonal to one another        such that a construction line going between the first port-pair        and a construction line going through the second port pair are        at 90 degrees to each other, and;    -   (b) an isolation element 102 that (i) receives the        antenna-system outputs, (ii) isolates the SoI on each port based        on the SoI-isolation-metrics in the user data, and (iii) has an        output with the isolated SoI corresponding to each        antenna-system output; and    -   (c) an estimator element 103 that (i) receives the isolated SoI        for each of the antenna-system ports from the isolation element,        and (ii) estimates and outputs the list of desired outputs        specified in the user data.

The list specifying desired outputs generally includes for eachparticular SoI, one or more items such as: the coordinate system, the RFemitter sensing system's pose (position & orientation) at the time ofmeasurement of the SoI level, time and date, which angles to output(e.g. azimuth, elevation, or both), desired azimuth angle accuracy andconfidence level, achieved azimuth angle accuracy and confidence level,desired elevation angle accuracy and confidence level, achievedelevation angle accuracy and confidence level, maximum processing timeallowed, processing time used, time periods used to integrate the SoIenergy, SoI polarization, center frequency, modulation type,peak-to-average ratio, variance, times to a number of the highest peaks,frequency-versus-time profile, power-versus-time profile, rms power,etc.

The antenna-system's port configuration includes items associated witheach port, such as the position and beam pattern (including one or moreof magnitude, polarization, group-delay, impulse-response, andtransfer-function as a function of angles) relative to a referenceposition/orientation on the RF emitter sensing system.

The estimator element is configured to determine and output anangle-of-arrival (AoA) estimate of a signal-of-interest (SoI) in amanner that is unbiased to homogeneous noise in the environment, and toits own system noise including the low noise amplifiers (LNA) in itsfront end.

The estimator element is also configured to mitigate finite tolerancesin antenna element dimensions and termination network impedances andlosses. The disclosed mitigation method enhances the RF emitter sensingdevice's accuracy by making it immune to manufacturing tolerances.

The antenna system, in some embodiments, is configured to use shadowingon all or some of the sensor elements. Any antenna element that is madesmall enough, can fit within a small/short shadow behind a smallreflective or absorptive barrier. Operation in this shadow region allowsreduced sensitivity to particular wave fronts, such as a skywave, whileretaining sensitivity to other wavefronts, such as a ground-wave. Thismodified sensitivity enhances the performance of the RF emitter sensingsystem in some applications, such as finding the AoA of near verticalincidence skywave (NVIS) signals. DPA, QPA, HPA, and DHPA elements areparticularly suitable to operate in a shadowed mode since they remaindirectional even at extremely small size.

In other words, the invention discloses the an RF emitter sensing deviceincluding an antenna circuit and an estimator configured to output, forone or more incoming signal-of-interest (SoI), either or both of anestimated range to the emitter of each SoI, and estimates for one ormore angles corresponding to the 3D angle-of-arrival (AoA) of each SoI,wherein the antenna circuit has a plurality of ports that each output anoutput signal containing the one or more SoI, the antenna circuitincluding one or more multi-port antennas, each multi-port antennahaving two or more ports, each multi-port antenna being configured topick up a combination of one or more E-field signals and one or moreH-field signals from each SoI, in a common volume of space; and theestimator element is configured to output either or both of an estimatedrange to the emitter of each SoI, and estimates for one or more anglescorresponding to the AoA of each SoI by receiving the output signalsfrom the antenna circuit, and generating either or both of an estimatedrange to the emitter of each SoI, and estimates for one or more anglescorresponding to the AoA of each SoI.

The invention also discloses the above RF emitter sensing device whereineach multi-port antenna is also (a) configured such that each port has anominally cardioid beam pattern in all planes containing a common axisof symmetry about the cardioid beam pattern, or (b) configured such thatthe one or more E-field signals and the one or more H-field signals canbe isolated from each other by combining the output signals, or (c)configured to pick up a combination of one or more E-field signals andone or more H-field signals from an SoI, such that, an output port on afirst-half of a multiport antenna picks up a sum of an E-field signaland H field signal, creating a sum signal, while an output port on another-half of the multiport antenna picks up a difference between anE-field signal and an H-field signal, creating a difference signal,wherein, the first-half of the multiport antenna is the half of theantenna that the SoI arrives at first, according to the Poynting vector,and the other-half of the multiport antenna is the half that is not thefirst half.

The invention also discloses the above RF emitter sensing device whereinthe estimator circuit is also configured to mitigate extraneous signalsand isolate one or more desired SoI from the antenna circuit's outputsignals.

The invention also discloses the above RF emitter sensing device alsoreceiving or having access to user data that includes SoI isolationparameters or characteristics corresponding to one or more user-desiredSoI wherein, the estimator element is configured to isolate the one ormore user-desired SoI from other extraneous signals according to theSoI-isolation-parameters. Examples of SoI-isolation-parameters for anSoI include time intervals, time intervals when the SoI is known orlikely to be active, time intervals when the SoI is known or likely tobe inactive, time-frequency profile intervals, field strength range,center frequency, bandwidth, modulation characteristics, occurrencetiming, repetition rate, polarization, stability of field strength,constraints on a range of potential angles of arrival, and multipathgeometries.

The invention also discloses the above RF emitter sensing device whereinreceiving or having access to user data including a list of desiredoutputs associated with an incoming signal, wherein: the list of desiredoutputs including either or both of an estimated range to the emitter ofeach SoI, and estimates for one or more angles corresponding to thePoynting vector of each SoI and may also include other metricsassociated with each SoI such as: the antenna element locations used,the distance between the antenna locations used, the field strength, thepose of the RF emitter sensing device relative to some other coordinatesystem at the time the antenna outputs were measured, the time periodsthe antenna outputs were used, the desired accuracy, the desiredconfidence level, the achieved accuracy, the achieved confidence level,the maximum processing time allowed, the processing time used, thepolarization of the SoI, the center frequency the SoI, the type ofmodulation on the SoI, the pulse repetition rate of the SoI if the SoIis pulsed, the peak-to-average ratio of the SoI over the period used,the variance in the SoI energy over the period used, a number Pm,representing the maximum peak level that occurred in the SoI during thetime period used, a number Pr representing a level range factor, anumber Npc that is the count of signal peaks that were within the rangeof Pm and Pm*Pr that occurred during the processing of the SoI, whereinNpc is governed by the user specifying Pr, or Pr is governed by the userspecifying Npc, the time that each of the Npc peaks occurred, thefrequency versus time profile of the SoI over the period used, the powerversus time profile of the SoI over the period used, wherein the powerunits are specified, such as being an rms, average, quasi-peak, peak,etc., one or more trigger signals, each indicating that a specific eventoccurred, and the time of occurrence of a specific event, whereinspecific events are specified, such as the occurrence of or end of atime-frequency-power profile, and the estimator element is configured togenerate and output the list of desired outputs

The invention also discloses the above RF emitter sensing device alsoreceiving or having access to user data t that includes orientationinformation including one or more of: a definition for a localcoordinate system on the RF emitter sensing device that includes asystem reference position on the RF emitter sensing device; an antennacircuit configuration definition that includes locations, orientations,and beam patterns associated with each of the plurality of antenna portsrelative to the local coordinate system on the RF emitter sensingdevice; and may also include other information such as time, date, andthe pose of the local coordinate system on the RF emitter sensing devicerelative to another coordinate system, such as an earth coordinatesystem, or a ground or an air vehicle coordinate system; and wherein abeam pattern definition includes the response as a function of angle forone or more of: polarization-versus-frequency; group-delay; transferfunction magnitude versus frequency; transfer function phase versusfrequency; and impulse response.

The invention also discloses the above RF emitter sensing device whereinthe one or more multi-port antennas include a multiport antenna that iscomprised of one or more conductive-surface-pairs, wherein, eachconductive-surface-pair has a first conductive surface, a secondconductive surface offset in an offset-direction from the firstconductive surface, and one or more port-pairs, each port-pair includinga first port and a second port; wherein each of the first and secondport is formed by a connection to the first and second conductivesurfaces, and wherein each of the one or more port-pairs forms a loopgoing from a first terminal of a corresponding first port, through thefirst conductive surface to a first terminal of a corresponding secondport, through a termination load connected across the correspondingsecond port to a second terminal of the corresponding second port, andthrough the second conductive surface to a second terminal of thecorresponding first port, and through a termination load connectedacross the corresponding first port, back to the first terminal of thecorresponding first port to complete the loop, and an output for eachport; and wherein the different conductive-surface-pairs have differentoffset-directions; and wherein the loops associated with the port-pairsshare a nominally common center point. The invention discloses the aboveRF emitter sensing device wherein all specific embodiments of thepreceding multiport antenna are permissible, including a multiportantenna with one conductive surface pair wherein the surface pairattaches to one port-pair, or two port-pairs, or two port-pairs whereinthere is an aiming axis associated with each port-pair, lying in theplane of the loop formed by each port-pair, that extends between eachport-pair such that it intersects the center point between the terminalsof the first port, and the center point between the terminals of thesecond port, wherein there is a polarization axis orthogonal to theaiming axis and lying in the plane of the loop formed by each port-pair,wherein the two port-pairs are oriented such that: their aiming axes arenominally orthogonal to each other, their polarization axes arenominally aligned to each other, and their loops nominally share thesame center point.

Similarly, the invention discloses the above RF emitter sensing devicewherein the above multiport antenna has three conductive surface-pairswherein each surface-pair attaches to one port-pair, wherein eachconductive-surface-pair has an offset direction and port-pair placementsuch that the aiming axes of the three port-pairs are nominallyorthogonal to each other and the polarization axes of the threeport-pairs are nominally orthogonal to each other, and the loops formedby the three port-pairs nominally share the same center point.

Similarly, the invention discloses the above RF emitter sensing devicewherein the above multiport antenna has three conductive surface-pairswherein each surface-pair attaches to two port-pairs, wherein eachconductive-surface-pair has an offset direction and port-pair placementsuch that the aiming axes of the the two port-pairs on each surface pairare nominally orthogonal to each other and the polarization axes arealigned, while the polarization axes of the ports on any conductivesurface pair is orthogonal to the polarization axis of the ports on theother conductive surface pairs, and the loops formed by all theport-pairs nominally share the same center point.

The invention also discloses the above RF emitter sensing device whereinthe estimator element is configured to output either or both of anestimated range to the emitter of the incoming signal, and estimates forone or more angles corresponding to the AoA of the incoming signal byalso computing the estimated range and/or one or more angle estimatesbased on a computation that is a function of the received output signalsfrom the antenna circuit.

The invention also discloses the above RF emitter sensing device whereinthe estimator element is configured to output either or both of anestimated range to the emitter of an SoI, and estimates for one or moreangles corresponding to the AoA of an SoI by also computing theestimated range and/or one or more angle estimates based on acomputation that is a function of: the received output signals from theantenna circuit, and a set of one or more baseline values determinedwith one or more known SoI, with each of the one or more known SoI atone or more known positions including one or more of a range and one ormore angles.

The invention also discloses the above RF emitter sensing device whereinthe estimator element is configured to output either or both of anestimated range to the emitter of an SoI, and estimates for one or moreangles corresponding to the AoA of an SoI by also: computing theestimated range and/or one or more angle estimates based on acomputation that is a function of: the received output signals from theantenna circuit, and a set of one or more baseline values determinedwith one or more known SoI, with each of the one or more known SoI atone or more known positions including one or more of a range and one ormore angles. The invention also discloses the preceding RF emittersensing device wherein the baseline values are stored.

The invention also discloses the above RF emitter sensing device whereinthe estimator element is configured to output either or both of anestimated range to the emitter of an SoI, and estimates for one or moreangles corresponding to the AoA of an SoI by also, computing theestimated range and/or one or more angle estimates based on acomputation that is a function that uses the received SoI from theantenna circuit output signals, wherein the function includes: computinga set of weighted sums, where each weighted sum is a sum of weightedversions of the SoI from two or more output signals received from two ormore ports of the antenna circuit, and wherein the weights can bepositive, negative, or complex.

The invention also discloses the above RF emitter sensing device whereinthe estimator element is configured to output either or both of anestimated range to the emitter of an SoI, and estimates for one or moreangles corresponding to the AoA of an SoI by also: computing theestimated range and/or one or more angle estimates based on acomputation that is a function that uses the received output signalsfrom the antenna circuit, wherein the function is configured to mitigateestimation bias caused by one or more of: receiver noise, noise pickedup by the antennas, noise picked up by antennas that is uncorrelatedbetween different ports, sensitivity imbalance in the E and H fieldspicked up by a port, the magnitude of an SoI, modulation of the SoI,effects of non-ideal termination impedances attached to the antennaports, and the effects of objects causing reflections into the antennacircuit or blockages to the antenna circuit.

The invention also discloses the above RF emitter sensing device whereinthe estimator element is configured to output either or both of anestimated range to the emitter of an SoI, and estimates for one or moreangles corresponding to the AoA of an SoI by also, computing theestimated range and/or one or more angle estimates based on acomputation that is a function that uses the received SoI from theantenna circuit output signals, wherein the function is configured tomitigate estimation bias caused by one or more of: receiver noise, noisepicked up by the antennas, noise picked up by antennas that isuncorrelated between different ports, sensitivity imbalance in the E andH fields picked up by a port, the magnitude of an SoI, modulation of theSoI, effects of non-ideal termination impedances attached to the antennaports, and the effects of objects causing reflections into the antennacircuit or blockages to the antenna circuit, by estimating an angle ofarrival from an (i,j) pair of port-pairs, where the function usesarguments including one or more ratios, A_(i)/B_(i) A_(j)/B_(j), andB_(i)/B_(j), and where the function may include trigonometric functions,lookup table based functions, and functions based on measurements of SoIat known angles, where the trigonometric functions include functionssuch as inverse sine, inverse cosine, inverse tangent and four quadrantarctangent functions, such as the Fortran a tan 2(y,x) function,wherein: the terms, A_(i), B_(i), A_(j), B_(j), are either:A_(i)=P_(i,1)−P_(2,i), B_(i)=P_(1,i)+P_(2,i), A_(j)=P_(1,j)−P_(2,j),B_(j)=P_(1,j)+P_(2,j), or A_(i)=P_(1,i)′−P_(2,i)′,B_(i)=P=P_(1,i)′+P_(2,i)′, A_(j)=P_(1,j)′−P_(2,j)′,B_(j)=P_(1,j)′+P_(2,j)′, and where i and j are indexes, each of whichrepresents a particular port-pair, where each takes on an integer valuefrom 1 to N, and N is the number of port-pairs in the antenna circuit,and the (i,j) pair of port-pairs is a set of ports comprised of thei^(th) port-pair and a j^(th) port pair, wherein, j is not equal to i,the ports in both port-pairs share the same polarization, the patternsof the first port and the second port in each of the port-pairs areaimed in opposite directions defining an aiming axis, the aiming axis ofthe i^(th) port-pair is orthogonal to that of the i^(th) port-pair, andwherein P_(1,j)′ is an initial SoI amplitude derived from the first portof the i^(th) port-pair, and similarly P_(1,j)′ is an initial SoIamplitude derived from the first port of the j^(th) port-pair, andwherein P_(2,i)′, is an initial SoI amplitude derived from the secondport of the i^(th) port-pair, and similarly P_(2,j)′ is an initial SoIamplitude derived from the second port of the j^(th) port-pair, andwherein a set of weighted sums is comprised of, a first quantity,P_(1,i) which is a corrected amplitude for the SoI at the first port ofthe i^(th) port-pair, and a second quantity P_(2,i), which is acorrected amplitude for the SoI at the second port of the i^(th)port-pair, and wherein the set of weighted sums is created as:P_(1,i)=(a_(i)+1)P_(1,i)′+(a_(i)−1)P_(2,i)′, andP_(2,i)=c_(i)[(b_(i)+1)P_(2,i)′+(b_(i)−1)P_(1,i)′] where: the weights inthe weighted sum are (a_(i)+1), (a_(i)−1), (b_(i)+1), and (b_(i)−1), andwhere a_(i) and b_(i) are chosen such that, for the SoI, the beampattern of P_(1,j) is cardiod with a single deep null in a firstdirection, the beam pattern of P_(2,i) is cardiod with a single deepnull in a second direction, wherein the first direction and seconddirection are nominally 180 degrees from each other, and c_(i). ischosen such that the peaks of the main lobes of P_(1,i) and P_(2,i) areequal.

The invention also discloses the above RF emitter sensing device whereinthe estimator element is configured to output either or both of anestimated range to the emitter of an SoI, and estimates for one or moreangles corresponding to the AoA of an SoI by also, computing theestimated range and/or one or more angle estimates based on acomputation that is a function that uses the received SoI from theantenna circuit output signals, wherein the function is configured tomitigate estimation bias caused by one or more of: receiver noise, noisepicked up by the antennas, noise picked up by antennas that isuncorrelated between different ports, sensitivity imbalance in the E andH fields picked up by a port, the magnitude of an SoI, modulation of theSoI, effects of non-ideal termination impedances attached to the antennaports, and the effects of objects causing reflections into the antennacircuit or blockages to the antenna circuit, by estimating an angle ofarrival from an (i,j) pair of port-pairs, where the function usesarguments including one or more of A_(i)(B_(i)−ξ_(i,j)),A_(j)/(B_(j)−ξ_(i,j)), and (B_(i)−ξ_(i,j))/(B_(i)−ξ_(i,j)), and wherethe function may include trigonometric functions, lookup table basedfunctions, and functions based on measurements of SoI at known angles,where the trigonometric functions include functions such as inversesine, inverse cosine, inverse tangent and four quadrant arctangentfunctions, such as the Fortran a tan 2(y,x) function, wherein: theterms, A_(i), B_(i), A_(j), B_(j), are either: A_(i)=P_(1,i)−P_(2,i),B_(i)=P_(1,i)+P_(2,i), A_(j)=P_(1,j) P_(2,j), B_(j)=P_(1,j)+P_(2,j), orA_(i)=P_(1,i)′−P_(2,i)′, B_(i)=P=P_(1,i)′+P_(2,i)′,A_(j)=P_(1,j)′−P_(2,j)′, B_(j)=P_(1,j)′+P_(2,j)′, and where i and j areindexes, each of which represents a particular port-pair, where eachtakes on an integer value from 1 to N, and N is the number of port-pairsin the antenna circuit, and the (i,j) pair of port-pairs is a set ofports comprised of the i^(th) port-pair and a j^(th) port pair, wherein,j is not equal to i, the ports in both port-pairs share the samepolarization, the patterns of the first port and the second port in eachof the port-pairs are aimed in opposite directions defining an aimingaxis, the aiming axis of the i^(th) port-pair is orthogonal to that ofthe j^(th) port-pair, and wherein P_(1,i)′ is an initial SoI amplitudederived from the first port of the i^(th) port-pair, and similarlyP_(1,j)′ is an initial SoI amplitude derived from the first port of thej^(th) port-pair, and wherein P_(2,i)′ is an initial SoI amplitudederived from the second port of the i^(th) port-pair, and similarlyP_(2,j)′ is an initial SoI amplitude derived from the second port of thej^(th) port-pair, and wherein a set of weighted sums is comprised of, afirst quantity, P_(1,i) which is a corrected amplitude for the SoI atthe first port of the i^(th) port-pair, and a second quantity P_(2,i),which is a corrected amplitude for the SoI at the second port of thei^(th) port-pair, and wherein the set of weighted sums is created as:P_(1,i)=(a_(i)+1)P_(1,i)′+(a_(i)−1)P_(2,i)′, andP_(2,i)=c_(i)[(b_(i)+1)P_(2,i)′+(b_(i)−1)P_(1,i)′] where: the weights inthe weighted sum are (a_(i)+1), (a_(i)−1), (b_(i)+1), and (b_(i)−1), andwhere a_(i) and b_(i) are chosen such that, for the SoI, the beampattern of P_(1,i) is cardiod with its single deep null in a firstdirection, and the beam pattern of P_(2,i) is cardiod with its singledeep null in a second direction, and the first direction and seconddirection are nominally 180 degrees from each other, and c_(i). ischosen such that the peaks of the main lobes of P_(1,i) and P_(2,i) areequal, and the factor to mitigate homogeneous noise, ξ_(i,j), can becomputed by functions including:

$\xi_{i,j} = {{\Phi \left( {A_{i},B_{i},A_{j},B_{j}} \right)} = {{Re}\left\lbrack {\frac{B_{i}}{2} + \frac{B_{j}}{2} - \sqrt{\frac{F}{6} + \frac{H}{4} + \frac{I}{144}} - \sqrt{\frac{F}{3} - \frac{H}{4} - \frac{I}{144} - \frac{3E}{\sqrt{I + {36H} + {24F}}}}} \right\rbrack}}$  wherein$\mspace{20mu} {{E = {{A_{i}^{2}B_{i}} - {A_{j}^{2}B_{i}} - {A_{i}^{2}B_{j}} + {A_{j}^{2}B_{j}}}},\mspace{20mu} {F = {A_{i}^{2} + {B_{i}^{2}/2} - {B_{i}B_{j}} + A_{j}^{2} + {B_{j}^{2}/2}}},\mspace{20mu} {G = {\left( {B_{i} - B_{j}} \right)^{2}\left( {{4A_{i}^{2}} - B_{i}^{2} + {2B_{i}B_{j}} + {4A_{j}^{2}} - B_{j}^{2}} \right)}},{H = \sqrt[\frac{1}{3}]{\begin{matrix}{{\sqrt{3\left( {{432E^{4}} - {64E^{2}F^{3}} + {G\left( {{16F^{4}} - {144E^{2}F}} \right)} + {8F^{2}G^{2}} + G^{3}} \right)}/72} +} \\{{E^{2}/2} - {F^{3}/27} + {{G\left( {{2B_{i}B_{j}} - {2A_{i}^{2}} - B_{i}^{2} - {2A_{j}^{2}} - B_{j}^{2}} \right)}/24}}\end{matrix}}},\mspace{20mu} {and}}$$\mspace{20mu} {I = \left\{ {\begin{matrix}{\left( {{4F^{2}} - {3G}} \right)/H} & {{{if}\mspace{14mu} H} \neq 0} \\0 & {{{if}\mspace{14mu} H} = 0}\end{matrix}.} \right.}$

The invention also discloses the above RF emitter sensing device whereinthe estimator element is configured to output either or both of anestimated range to the emitter of an SoI, and estimates for one or moreangles corresponding to the AoA of an SoI by also: computing theestimated range and/or one or more angle estimates based on acomputation that is a function that uses the received output signalsfrom the antenna circuit, wherein the function is configured to mitigateestimation bias caused by receiver noise and noise picked up by theantennas, by coherently deriving the amplitude of the SoI on each port,by correlating the signal from each port in a port pair, over a timeperiod which may be continuous or discontinuous, with a signal that is acombination of the signals from one or more ports that do not includethe ports in the port-pair, where the combination of signals includes,selecting one or more porta and summing their signals, selecting one ormore ports and weighting and summing their signals, selecting the portwith the largest signal from among the available ports and using itssignal, and using maximum ratio combining (MRC) to weight and sum thesignals from two or more of the ports.

The invention also discloses the above RF emitter sensing device whereinthe estimator means is configured to output either or both of anestimated range to the emitter of an SoI, and estimates for one or moreangles corresponding to the AoA of an SoI by also using one or more of:one or more magnitudes from one or more combinations of the outputsignals from among the different ports of the antenna circuit, and oneor more phases from one or more combinations of the output signals fromamong the different ports of the antenna circuit. The invention alsodiscloses the preceding RF emitter sensing device wherein the aboveweights applied to the one or more combinations are stored. Theinvention also discloses the preceding RF emitter sensing device whereinthe one or more combinations of output signals includes combinationsthat isolate the E-field of the SoI and that isolate the H-field of theSoI.

The invention also discloses the above RF emitter sensing device whereinthe antenna circuit is configured to pick up signals at a more than onelocation or orientation, and the one or more locations or orientationsare made with one or more of a sequential configuration and asimultaneous configuration; wherein, in the sequential configuration,ports are in respective initial locations and orientations at an initialtime, and ports are in a respective next location and orientation at anext time that is later than the initial time, and wherein the estimatoruses the output signals received at different times.

The invention also discloses an RF emitter sensing device comprising anantenna circuit, an isolation element, and an estimator elementconfigured to output, for one or more incoming signal-of-interest (SoI),either or both of an estimated range to the emitter of each SoI, andestimates for one or more angles corresponding to the angle-of-arrival(AoA) of each SoI, wherein: the antenna circuit has a plurality of portsthat each output an output signal containing the one or more SoI, theantenna circuit including one or more multi-port antennas, eachmulti-port antenna having two or more ports, each multi-port antennabeing configured to pick up a combination of one or more E-field signalsand one or more H-field signals from each SoI, in a common volume ofspace, such that the one or more E-field signals and the one or moreH-field signals can be isolated from each other by combining the outputsignals; and the isolation element is configured to output one or moreisolated SoI outputs, for each respective port by receiving the outputsignals from each output port of the antenna circuit, and isolating ineach respective port, one or more SoI from other extraneous signals; andthe estimator element is configured to output either or both of anestimated range to the emitter of each SoI, and estimates for one ormore angles corresponding to the AoA of each SoI by: receiving theoutput signals from the isolation element, and generating either or bothof an estimated range to the emitter of each SoI, and estimates for oneor more angles corresponding to the AoA of each SoI.

The invention also discloses the preceding RF emitter sensing devicewherein the estimator element is configured to output either or both ofan estimated range to the emitter of an SoI, and estimates for one ormore angles corresponding to the AoA of an SoI by also: computing, foreach SoI, a set of measured values based on the one or more isolated SoIoutputs from the isolation element, comparing, for each SoI, the set ofmeasured values with a plurality of sets of calibration values, wherethe plurality of sets of calibration values is comprised of sets ofvalues determined with the SoI emitter at a known, one or more of,location, AoA, and range.

The invention also discloses the preceding RF emitter sensing devicewherein the one or more multi-port antennas include a multiport antennathat is comprised of one or more conductive-surface-pairs, wherein, eachconductive-surface-pair has a first conductive surface, a secondconductive surface offset in an offset-direction from the firstconductive surface, and one or more port-pairs, each port-pair includinga first port and a second port; wherein each of the first and secondport is formed by a connection to the first and second conductivesurfaces, and wherein each of the one or more port-pairs forms a loopgoing from a first terminal of a corresponding first port, through thefirst conductive surface to a first terminal of a corresponding secondport, through a termination load connected across the correspondingsecond port to a second terminal of the corresponding second port, andthrough the second conductive surface to a second terminal of thecorresponding first port, and through a termination load connectedacross the corresponding first port, back to the first terminal of thecorresponding first port to complete the loop, and an output for eachport; and different conductive-surface-pairs have differentoffset-directions and the loops associated with the port-pairs share anominally common center point.

The invention also discloses the above RF emitter sensing deviceswherein the antenna circuit is configured such that the ports, includingthose from one or more multiport antennas, can be combined to providethree orthogonal E-field terms and three orthogonal H-field terms (e.g.E_(X), E_(Y), E_(Z) and H_(X), H_(Y), H_(Z)), and the estimator isconfigured to estimate the three dimensional Poynting vector of each SoIfrom the antenna circuit's outputs and output the three dimensional AoAfor each SoI.

The invention also discloses the preceding RF emitter sensing devicealso receiving or having access to user data that includesSoI-isolation-parameters corresponding to each SoI wherein, theisolation element is configured to isolate the one or more SoI fromother extraneous signals according to the SoI-isolation-parameters. Theinvention also discloses the preceding RF emitter sensing device whereinthe SoI-isolation-parameters include one or more of, time intervals whenthe SoI is known or likely to be active, time intervals when the SoI isknown or likely to be inactive, field strength range, center frequency,bandwidth, modulation characteristics, occurrence timing, repetitionrate, polarization, field strength range, stability of field strength,constraints on a range of potential angles of arrival, and multipathgeometries.

The invention also discloses the preceding RF emitter sensing devicewherein the estimator element is configured to output either or both ofan estimated range to the emitter of an SoI, and estimates for one ormore angles corresponding to the AoA of an SoI by also computing theestimated range and/or one or more angle estimates based on acomputation that is a function of the received output signals from theantenna circuit, and a set of one or more baseline values determinedwith one or more known SoI, with each of the one or more known SoI atone or more known positions including one or more of a range and one ormore angles. The invention also discloses the preceding RF emittersensing device wherein the baseline values are stored.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying figures, where like reference numerals refer toidentical or functionally similar elements and which together with thedetailed description below are incorporated in and form part of thespecification, serve to further illustrate an exemplary embodiment andto explain various principles and advantages in accordance with thepresent invention.

FIG. 1A is a block diagram of an RF emitter sensing system;

FIG. 1B is a block diagram of an RF emitter sensing system similar toFIG. 1A but with an explicit isolation element.

FIG. 2A is a picture of a transmission line version of a DPA;

FIG. 2B is a picture showing an array of two transmission line versionDPA antennas oriented at 90 degrees to each other according to adisclosed embodiment, where each antenna element is similar to the oneshown in FIG. 3;

FIG. 3 is a mechanical drawing of a transmission line version DPA wherethe two ports share a common spatial aperture that produces oppositefacing cardioid patterns from the two ports for use in the RF emittersensing system according to a disclosed embodiment;

FIG. 4 is a mechanical drawing of a transmission line version DPA in anunbalanced configuration;

FIG. 5 is a mechanical drawing for a 100 ohm balanced cylindrical DPA;

FIG. 6 is a mechanical drawing showing a nominally spherical quad-portantenna (QPA) that is a pair of DPAs that are oriented orthogonally toeach other and that share the same conductive surfaces;

FIG. 7 is a mechanical drawing for a alternative embodiment of a QPAconstructed almost identically as the spherical QPA, but is cubicalinstead of spherical;

FIG. 8 shows a balanced DPA with its top covered by an absorbing and/orreflective layer which shields or shadows the antenna;

FIG. 9 shows a balanced DPA with both its top and its bottom covered byabsorbing and/or reflective layers which shield or shadow the antennafrom waves coming down toward the top of the antenna, or coming uptoward the bottom of the antenna useful for elevated applications suchas on aircraft;

FIG. 10 shows an unbalanced DPA with its top covered by an absorbing andor reflective layer, which shield or shadow the antenna from wavescoming down toward the top of the antenna;

FIG. 11 is a drawing illustrating the theory of operation of a DPA,including showing a side view of a DPA along with solid or dashed arrowsto illustrate a wave coming directly into either the right (dashed) orleft (solid) ports of the antenna, along with the direction of thecurrent induced by the magnetic field, and the voltage induced by theelectric field, according to a disclosed embodiment;

FIG. 12 shows an antenna-system with sixteen ports;

FIG. 13 shows an embodiment with an antenna-system comprised of 18ports, an isolation element with 18 parallel channels, including aswitch network and calibration signal generator that allow full systemcalibration as well as built-in test capability to confirm all wiring;

FIG. 14 shows a low-cost embodiment in which the antenna-system has 14ports, the isolation element has only two coherent receivers andincludes a switch network that allows any antenna to connect to eitherreceiver and allows system calibration;

FIG. 15 illustrates the spherical coordinate system used to express theDPA's output voltage versus the angle and polarization of the incomingwave;

FIG. 16 illustrates magnitude patterns when ε(λ) is positive, negative,or ideal, where ε(λ) represents an imbalance between the electric dipolemoment and the magnetic dipole moment, or an error caused by a phaseshift due to operating the DPA at a high frequency;

FIG. 17 shows a theoretical pattern along with overlaid measured pointsshowing the very close match between the theoretical 2-parameter modeland the measured beam pattern shape in the critical 45 to 135 degreesector according to a disclosed embodiment;

FIG. 18 is a plot showing the error between a simple 2-parametertheoretical beam pattern and the measured beam pattern according to adisclosed embodiment;

FIG. 19A is a mechanical drawing showing a 6-port {right arrow over (p)}cross {right arrow over (m)} antenna (6-PA) also called a hex portantenna (HPA) that is cubical, which can replace three DPAs that areoriented orthogonally to each other;

FIG. 19B is a mechanical drawing showing a 12-port {right arrow over(p)} cross {right arrow over (m)} antenna (12-PA) also called a dual hexport antenna (DHPA) that is cubical, which can replace three QPAs thatare oriented orthogonally to each other; and

FIG. 20 is a three-dimensional drawing with rectangular-boxrepresentations of three DPAs similar to those in FIG. 3, oriented toenable their six ports to collect all six EM components. Following fromFIG. 11, electromagnetic components E_(x), E_(y), E_(z) shown in FIG. 20create a voltage across the two conductive surfaces in the threerespective DPAs. Currents I_(x), I_(y), I_(z) induced in the loop formedby the ports and the conductive surfaces in the respective DPAs resultfrom the respective H-field components H_(x), H_(y), H_(z), shown inFIG. 20.

DETAILED DESCRIPTION

The instant disclosure is provided to further explain in an enablingfashion the best modes of performing one or more embodiments of thepresent invention. The disclosure is further offered to enhance anunderstanding and appreciation for the inventive principles andadvantages thereof, rather than to limit in any manner the invention.The invention is defined solely by the appended claims including anyamendments made during the pendency of this application and allequivalents of those claims as issued.

It is further understood that the use of relational terms such as firstand second, and the like, if any, are used solely to distinguish onefrom another entity, item, or action without necessarily requiring orimplying any actual such relationship or order between such entities,items or actions. It is noted that some embodiments may include aplurality of processes or steps, which can be performed in any order,unless expressly and necessarily limited to a particular order; i.e.,processes or steps that are not so limited may be performed in anyorder.

Much of the inventive functionality and many of the inventive principleswhen implemented, may be supported with integrated circuits (ICs), RFamplifiers, RF switches, mixers, analog-to-digital converters,digital-to-analog converters, direct digital synthesis (DDS) ICs, phaselocked loop (PLL) and voltage controlled oscillator (VCO) ICs,microcontrollers, microprocessors, field programmable logic array (FPGA)ICs, digital signal processing (DSP) ICs, dynamic random access memory(DRAM) devices, static random access memory (SRAM) devices, or the like.In particular, they may be implemented using semiconductor processes andtransistors such as FET, (including HFET, HEMT, E-PHEMT, PHEMT, MESFET,JFET, MOSFET, CMOS, etc.), BJT (including HBT, etc), and BiCMOS. It isexpected that one of ordinary skill, notwithstanding possiblysignificant effort and many design choices motivated by, for example,available time, current technology, and economic considerations, whenguided by the concepts and principles disclosed herein will be readilycapable of generating the required circuitry with minimalexperimentation. Therefore, in the interest of brevity and minimizationof any risk of obscuring the principles and concepts according to thepresent invention, further discussion of such ICs will be limited to theessentials with respect to the principles and concepts used by theexemplary embodiments.

Overview

Disclosed is an ultra miniature RF emitter sensing device that doespassive ranging and provides EM wave properties such as theAngle-of-Arrival (AoA) and polarization. It uses (1) an antenna systemthat includes unique miniature space-saving multi-port {right arrow over(p)} cross {right arrow over (m)} antenna (PxMA) elements that maintaintheir {right arrow over (p)} cross {right arrow over (m)} highdirectivity at arbitrarily low frequencies, and (2) signal processingmethods that operate on the antenna system's outputs such that they (a)enable self sensitivity calibration, (b) mitigate self noise, (c)mitigate homogeneous environmental noise, (d) mitigate multipath such asfrom sky-wave versus ground-wave paths and such as from nearby metalstructures, and (e) enable accurate AoA, polarization, and range toemitter characterization of signals so weak that they are below thenoise floor of, and cannot be received by, a standard receiver intendedto receive and demodulate the signal of interest. The resulting RFemitter sensing device can be extremely small size suitable for portableapplications. It also has lower complexity than previous systemsattempting to offer a similar bandwidth and frequency band of operation.Disclosed are miniature space-saving 4-port, 6-port, and 12-port PxMAantennas that maintain their {right arrow over (p)} cross {right arrowover (m)} high directivity to arbitrarily low frequencies. The 12-portand 6-port antennas provide all six E and H field components. Most RFapplications, including previous DF systems, use one or both of twoconstitutive antenna elements, the magnetic loop antenna element that issensitive to the H-field, which is sometimes implemented as a slotantenna, and the electric dipole/monopole antenna element that issensitive to the E-field. Previously combinations of these elementscreated “{right arrow over (p)} cross {right arrow over (m)} in apassband” antennas. The problem with these combined element antennas isthat the termination impedances and sensitivities of the two elementsare different and the network connecting them do not allow them tooperate with high directivity to arbitrarily low frequency—thus theirbandpass characteristic. There exists, however, a third constitutiveelement that has precisely collocated electric dipole and magneticmoments {right arrow over (p)} and {right arrow over (m)} respectively,and where the sensitivity to the E and H fields are inherently matchedand where a simple resistive termination allows them to be highlydirectional (i.e. high front-to-back ratio) to arbitrarily lowfrequency—which means their direction finding ability at low frequenciesdoes not degrade no matter how small this PxMA element is. Furthermore,the cardioid radiation pattern is rotationally symmetric about the axisof maximum radiation to arbitrarily low frequency. In other words, anE-plane cut and H-plane cut, or any cut going through the axis ofmaximum and minimum radiation, are identical. This symmetry propertyfacilitates measuring a wave's polarization along with itsangle-of-arrival. Disclosed is the use of this element, includingdisclosed miniature space-saving multi-port versions, in an RF emittersensing system that includes disclosed signal processing methodsallowing it to operate with high accuracy at low, for example HF (1-30MHz) frequencies, yet be smaller and lighter than previously thoughtpossible, such as being hand carried.

Definition of Antennas—PxMA, DPA

In 1971 Reference 9 (SSN-125), in equation 12.27 on page 150 describedthe properties that make an ideal {right arrow over (p)} cross {rightarrow over (m)} antenna (PxMA), where {right arrow over (p)} refers tothe electric dipole moment and {right arrow over (m)} refers to themagnetic dipole moment. It is a radiator that (a) has collocatedmagnetic and electric dipole moments {right arrow over (m)} and {rightarrow over (p)} respectively, and (b) these moments are related in thelate time (i.e. in the limit, at time goes to infinity) such that {rightarrow over (m)}=c{right arrow over (p)}, where c is the speed of light.Reference 10 (SSN-243) states, An “ideal {right arrow over (p)} cross{right arrow over (m)} radiator has some unique features that are notfound in other elemental radiators. They are summarized in part asfollows: (a) Cardioid radiation pattern rotationally symmetric with theaxis of maximum radiation. (b) Purely real power out flowing from anyspherical surface enclosing the source region. (c) Twice the directivityof a purely electric or magnetic dipole.” The “other elementalradiators” referred to in the above quote refer to the previouslymentioned dipoles/monopoles for electric fields, and loops for magneticfields. A key feature of the PxMA is that its “late time” cardioidbehavior extends, in the limit, to infinite time. This fact means thatin the frequency domain, its cardioid behavior is extremely widebandwidth and extends, in the limit, to DC. By using it in a small RFemitter sensing system, an RF emitter sensing system can be constructedthat is inherently broad band and works to arbitrarily low frequencieswithout any dependence on matching networks or tuning. Reference 9through Reference 16 address the theory, properties, and exampleconstructions of PxMA elements.

We will use the term “DPA” to refer to a dual-port {right arrow over(p)} cross {right arrow over (m)} antenna element that operates withhigh directivity to arbitrarily low frequency. In other words, a “DPA”is a PxMA with two ports, or a port-pair. Reference 11 (SSN-319)describes an embodiment of such a DPA where the cardioid patterns fromthe two ports are aimed opposite one another. In this case the antennais made with two conductive surfaces oriented and shaped so they can bethought of as a transmission line. FIG. 2A is a picture of an embodimentof this DPA. FIG. 2B pictures a mockup of a pair of these DPAs orientedin orthogonal directions and sharing a common vertical polarization,where one DPA's port-pair aims north and south, and the other DPA'sport-pair aims east and west. FIG. 3 is a mechanical drawing of the DPApictured in FIG. 2A.

FIGS. 2A, 2B, and 3 show the DPA in a balanced configuration. Theantenna element can be described as a pair of conductive surfaces offsetfrom one another with a pair of ports, where each port is formed by aconnection to the two conductive surfaces such that a loop is formedgoing from the first terminal of the first port, through the firstconductive surface to the first terminal of the second port, through thesecond port to the second terminal of the second port, and through thesecond conductive surface to the second terminal of the first port, andthrough the first port back to the first terminal of the first port tocomplete the loop. In FIG. 3, the pair of conductive surfaces are 305and 310. In FIG. 4, the pair of conductive surfaces are 305 and 460. InFIG. 5, the pair of conductive surfaces are 505 and 510. Theconfiguration of FIG. 3 is described in Reference 11. The configurationof FIG. 5 is described in Reference 15. The width of theseconfigurations can be narrowed by making the port connections not on theedges of the conductive surfaces.

In FIG. 3 the conductive surfaces might be thought of as a transmissionline with a top-wire 305 running left and right, and a bottom-wire 310running left and right, where the ratio of separation between the wiresand the width of the wires determine the transmission line impedance.When the width of both lines are the same, the transmission line isbalanced. The plane between and parallel to the antenna's conductiveplates (in other words, between the positive and negative terminals ofthe ports) is its ground-symmetry plane since the conductor above thesymmetry plane the conductor below the symmetry plane are a mirror imageof one another. Each end of the transmission line 340A and 340B is abalanced port. The dimensions given in FIG. 3 produce a 100 ohm balancedport that can be connected via a 100 ohm twinlead to a receiver. To usea standard unbalanced 50 ohm coaxial cable 325 and 330, the balancedport can be connected through a balun, (i.e. transformer or a splitter)315 and 320 as is shown in FIG. 3. For example, in the 1-750 MHz range,a MinCircuits SBTCJ-1WX would be suitable to use for the baluns 315 and320. The polarities on the baluns 315 and 320 are shown such that avertically polarized wave coming into the side of the antenna produces abalanced differential signal on the two output coaxial cables 325 and330. A vertically polarized wave arriving on the main beam axis at 340Acouples to cable 325, but does not couple to cable 330, providingexcellent back-to-front ratio. A wave coming straight down from the sky,polarized so that the E-field is aligned to the axis going through bothantenna ports, couples to both output coaxial cables 325 and 330 as acommon mode signal.

In FIG. 3, symbols 350 and 355 are used in schematics such as FIGS. 12,13, and 14, to represent the two ports and the orientation of aparticular antenna element port. The intent is for the symbols to conveythe polarization and directionality of a particular physical element.

FIG. 4 is a mechanical drawing of this DPA in its unbalancedconfiguration. In this case the two conductive surfaces 305 and 460 arenot the same size. The transmission line top-wire 305 running left andright, and a bottom-wire 460 running left and right, are not the samesize. Conductive surface 460, due to its larger size, can be called a“ground-plane” and therefore the transmission line would be calledunbalanced. This configuration is effectively one half (i.e. the tophalf) of the FIG. 3 configuration, where conductive surface 460 is inthe position of the ground symmetry plane of the FIG. 3 configuration.The width of 460 should extend beyond 305 by about the height shown inFIG. 3. As before, the ports of the antenna are at the left and rightends of the transmission line, i.e. the edges of conductive surface 305.The dimensions given in FIG. 4 produce 50 ohm ports that can beconnected to standard 50 ohm coaxial cables 325 and 330. These cablesare typically terminated into a receiver that provides a 50 ohm match.

Any mismatch reflection off of the receiver will travel back through theantenna to the other antenna port, and thereby reduce the inherentlyexcellent back-to-front ratio of the DPA element. If the receiver'scomplex reflection coefficient (e.g. S11) is known at any frequency ofinterest, and the cable 325, 330 electrical lengths and attenuation areknown, then calibrations can be applied to restore the inherentlyexcellent back-to-front ratio of the DPA element.

FIG. 11 illustrates the theory of operation of the DPA. It shows a sideview of a DPA along with solid 1105 and dashed 1110 arrows to illustratea wave coming directly into either the right and left portsrespectively. It also shows the direction of the current loop induced bythe magnetic field with a solid 1115 and dashed 1120 curved arrowsassociated with waves 1105 and 1110 respectively. It also shows thevoltage 1125 induced by the electric field, which is the same for bothwaves 1105 and 1110. By design, the magnetic and electric fields cancelat one port, and at the other port (where the wave arrives), add totwice what the E-field or H-field would have produced on their own Theantenna's inductance is adjusted with the loop area (i.e. with lengthand height). The antenna's capacitance, that is, between the conductivesurfaces 305 and 310 is adjusted with surface area and height. Thetermination impedance is set by the inductance and capacitance andmatched by designing the balun transformers and low noise amplifier(LNA) to have the desired input impedance. The induced current andvoltage add to produce an output voltage that is twice what the E-fieldor H-field would have produced on their own. It shows axes to illustratethe right-hand rule applied to the cross-product to get the Poyntingvector from the E cross H, and the right hand rule to get the clockwiseor counter-clockwise induced current from the H field direction;

The loop area defined by the height of the transmission line and thelength enclosed by the pair of port establishes the magnetic dipolemoment of the PxMA. The electric dipole moment of the PxMA is governedby the spacing between the two conductors (i.e. the height of theantenna element) and the capacitance across the ports, which is afunction of the size and shape of the two conductors. When the lengthand width and height and termination impedances are adjustedappropriately, as described in Reference 11, the end result is a dualport PxMA element, or DPA that maintains its unique PxMA properties toarbitrarily low frequencies, and with no matching network—just aresistive termination. Both ports have a cardioid pattern, and thecardioid pattern is rotationally symmetric about the main beam axis.

Reference 15 (SSN-441) describes a DPA that is similar to the one inReference 11, but the conductive surfaces are cylindrical and do notform a transmission line. FIG. 5 is a mechanical drawing for a 100 ohmbalanced cylindrical DPA. Like FIG. 3, there is a top conductive surface505, a bottom conductive surface 510, with ports 340A and 340B at theedges of these conductive surfaces. Coaxial cables 325 and 330 take thesignals from these ports to receivers that can isolate different signalsfrom one another. The cylinder radius sets the loop area and effectiveheight. The width of the conductive surfaces sets the capacitance. Likethe DPA of FIG. 3, the loop area, capacitance, and terminationresistance are set so that in the late time (i.e. as time goes toinfinity), {right arrow over (m)}=c{right arrow over (p)}. The magneticand electric dipole moments {right arrow over (m)} and {right arrow over(p)} are related by the speed of light c such that {right arrow over(m)}=c{right arrow over (p)} so that each port generates a cardioidpattern that extends to arbitrarily low frequency without any frequencydependent matching network but with a simple fixed non-reactivetermination. Like the DPA of FIG. 3, the plane between and parallel tothe antenna's conductive surfaces (in other words, between the positiveand negative terminals of the ports) is its ground-symmetry plane sincethe conductor above the symmetry plane the conductor below the symmetryplane are a mirror image of one another. Its cardioid pattern issymmetric along the axis of the main beam. Just as the balanced DPA ofFIG. 3 has an unbalanced version, as shown in FIG. 4, the balancedcylindrical DPA of FIG. 5 also has an unbalanced version where the lowerconductor 510 is replaced by a larger surface that serves as aground-plane, allowing the antenna to be half the height.

The DPA is electrically small and generally lightweight and inexpensivedue to its simple construction. The antenna ports are directional byvirtue of the fact that the antenna is a PxMA—the antenna's loop area,sensitive to the H-field, and antenna's electric dipole moment (oreffective height), sensitive to the E-field, are inherently matched toproduce the same voltage across a resistive port termination impedance.The termination, in the case of an RF emitter sensing system, is theinput impedance of the receiver connected to the port. Because of itsinherently matched E and H sensitivity at each port, the sum of theE-field induced signal and the H-field induced signal creates a null inone direction and creates a maximum response in the oppositedirection—i.e. the cardioid pattern ascribed to a PxMA. Because they area true PxMA they have high directivity regardless of how low thefrequency is—in other words, they are not a structure with a passbandnature, but could be infinitesimally small and still be directional.Both ports share the exact same co-located magnetic and electric dipolemoments at arbitrarily low frequency. The fields coupled to each portcome from the exact same spatial volume. As a result, their port ratiosare inherently matched ports and they have a highly repeatable andstable ratio of gains at any angle. If, due to manufacturing tolerances,a DPA is slightly larger or smaller, the ports still share the exactsame spatial aperture and volume and therefore have inherently matchedgain and symmetrical patterns, even though the null in the cardioid maynot be ideal. Because the sensitivity to mechanical tolerances is low,multiple DPAs are extremely well matched to each other, making themideal for use in phased-array structures. In other words, all of thesignal processing methods applied to arrays, such as those described inReference 5 can be applied to an array that includes DPA elements.

Derived from Reference 15, the output voltage of a DPA versus frequencyand the incidence angle of an incoming E-field follows the followingproportion:

$\begin{matrix}{{{V_{out}\left( {f,\varphi,\rho,{{port\_}1}} \right)} \approx {\frac{\pi \; A}{\lambda}\left( {1 + {\cos \; \theta}} \right)\left( {{E_{\theta}\sin \; \varphi} + {E_{\varphi}\cos \; \varphi}} \right)}}{{V_{out}\left( {f,\varphi,\rho,{{port\_}2}} \right)} \approx {\frac{\pi \; A}{\lambda}\left( {1 - {\cos \; \theta}} \right){\left( {{E_{\theta}\sin \; \varphi} + {E_{\varphi}\cos \; \varphi}} \right).}}}} & (1)\end{matrix}$

In this equation, A is the loop area of the antenna in square meters, λis the wavelength in meters, incident E-field (E_(φ),E_(θ)) has units ofvolts/m, and V_(out) is in volts. The angles φ and θ are expressed inthe spherical coordinate system such as that shown in FIG. 15. Forexample, referring to FIG. 15, suppose the X-Y plane is parallel to theearth's surface, with the Y-axis aimed north. Suppose the DPA isoriented so that its ports are on the Z-axis and its ground symmetryplane is the Z-X plane. To be clear, the DPA is oriented so that itsfirst port, at positive Z, aims up toward the sky; its second port, atnegative Z, aims down to the center of the earth; and the main beam fromthese ports is sensitive to a wave polarized with its E-field orientedalong the y-axis, or north-south. The angle θ is the angle to the sourceof the incident field relative to the aiming axis running through thetwo ports. At θ=0° the incident field arrives in the main beam of thefirst port. Note how, in Equation 1, regardless of φ, the beam patternis always a raised cosine function of θ. This perfect symmetry about φis useful for DF. We can define a plane that intersects both antennaports and the source of the incident field which we will call theφ-plane. This φ-plane can be visualized at a particular φ by imagining θspinning 360 degrees to define the φ-plane. The orientation of theincident E-field (i.e. its polarization) is given in relation to thisφ-plane. When φ=0° the φ-plane is the ground-symmetry plane. Theincident TEM (transverse electric magnetic) wave has E-field componentsthat are perpendicular to the direction of energy flow (i.e. thePoynting vector) with one component, E_(θ), in the φ-plane, and theother component, E_(φ), perpendicular to the φ-plane. Note that thesymmetry about the Z-axis is such that if the polarization were alwaysoriented for the maximum response, the output voltage would beindependent of φ and only depend on θ.

To illustrate the antenna's response, rotate the coordinate system andsuppose a DPA is oriented so that the first port aims north withvertical polarization. In this case, referring to FIG. 15, the Z-axiswould point to the north, the Z-X plane would represent the surface ofthe earth as well as the antenna's ground-symmetry plane, and the y-axiswould aim toward the sky while the x-axis would aim west. In thisvertical polarization case, an E-plane pattern is in a vertical planecontaining both ports (i.e. the Z-Y plane), and the H-plane pattern is ahorizontal plane that contains both ports (i.e. the Z-X plane).

Using this geometry, consider an E-plane beam pattern. In this case,φ=90° and θ spins 360 degrees to create the E-plane pattern. Here, θrepresents the elevation angle. At φ=90°, the φ-plane is the E-plane andwith vertical polarization E_(φ)=0 and the E-field is simply E_(θ). Notethat E_(θ) is vertical to the earth (and coming from the horizon) whenθ=0° but when θ=90°, it is coming down from the sky, is horizontal tothe earth (with no vertical component), and is aligned north-south alongthe axis running between the two DPA ports. At θ=45°, E_(θ) is stillcoming from the north, but is coming down from the sky and tilted at anangle of 45°. At θ=180° the E-field is coming from the south at thehorizon. E_(φ)=0 since there is no E-field perpendicular to the φ=90°φ-plane. Since E_(φ)=0, Equation 1 shows that the E-plane pattern is

$\begin{matrix}{{V_{out}\left( {f,\theta} \right)} \approx {\frac{\pi \; A}{\lambda}\left( {1 + {\cos \; \theta}} \right){E_{\theta}.}}} & (2)\end{matrix}$

Next consider an H-plane beam pattern. In this case φ=0°, and θ spins360 degrees to create the H-plane pattern. In this case θ represents theazimuth (or bearing) angle. All fields in this plot come from avertically polarized wave coming from the horizon. Since the verticallypolarized E-field is perpendicular to the φ=0° φ-plane, the E-field issimply E_(φ). In other words, since there is no horizontal E-field, i.e.no field in the φ-plane, E_(θ)=0. At θ=0°, the field is vertical to theearth and coming in from the north directly into the first port. Atθ=90°, the E-field is coming from the west. In this case, Equation 1shows that the H-plane pattern is

$\begin{matrix}{{V_{out}\left( {f,\theta} \right)} \approx {\frac{\pi \; A}{\lambda}\left( {1 + {\cos \; \theta}} \right)E_{\varphi}}} & (3)\end{matrix}$

A subscript nomenclature will be used to specify that a voltage camefrom a particular port orientation. For example, a receiver capable ofisolating a signal of interest (SoI) connected to port-P has an outputvoltage on it of ν_(P)(t) where t denotes time and P denotes the port.With earth centric compass aligned ports, the nomenclature includes portPε{N_(V), S_(V), E_(V), W_(V)} respectively referring to north, south,east, west, and vertically polarized, Pε{N_(H), S_(H), E_(H), W_(H)}respectively referring to north, south, east, west, and horizontallypolarized, and Pε{U_(N), D_(N), U_(E), D_(E)} respectively referring toup-north, (sensitive waves polarized north-south coming from the sky),down-north (sensitive waves polarized north-south coming from theground), up-east (sensitive to an east-west polarized wave coming fromthe sky), down-east (sensitive to an east-west polarized wave comingfrom the ground). For example, for a north-south oriented and verticallypolarized DPA, the receiver connected to port-N (the north port) has anoutput voltage of ν_(N) _(V) (t), while a receiver connected to thesouth port has an output voltage of ν_(S) _(V) (t). For brevity, whendiscussing a specific or representative case, like using a set ofantennas that have only vertically polarized ports, these will beshortened to just ν_(N)(t) and ν_(S)(t), since vertical polarization isunderstood in the context of their use. Similarly, when simply referringto a single arbitrarily aimed DPA pairs (ν_(N)(t), and ν_(S)(t)) or(ν_(E)(t) and ν_(W)(t)) or (ν_(U)(t) and ν_(D)(t)) will be used torepresent the oppositely aimed port-pairs, regardless of how they mightactually be aimed in a fielded system. The earth-centriccompass-oriented nomenclature is used for simplicity and clarity.Clearly any particular set of ports can be rotated to any orientationwhich can be mathematically specified by standard geometrictranslation/rotation equations.

Antenna System

In one simple embodiment, the antenna-system is comprised of a singleDPA element with two ports. Following FIG. 1A, the estimator element isconfigured to perform a function F that produces an AoA estimate fromthe outputs of the two DPA ports. Following FIG. 1B, the isolationelement filters out all signals except for each of the one or moresignals of interest (SoI) from each of the two DPA ports, and then theestimator element performs a function F that produces an AoA estimatefor each of the isolated SoI. The isolation element can be comprised ofa tuned filter or receiver at each port that isolates the SoI from othersignals.

This simple single-DPA embodiment is useful when the operator can rotatethe antenna, or when it is known that the AoA can only come from aparticular side of the DPA. When it is known that the AoA can only comefrom a particular side of the DPA, the function F can use a port-pairmeasurement at a single DPA orientation to determine the AoA. When theAoA can come from either side of the DPA, the DPA can be rotated so thatthe function F can use measurements from more than one DPA orientationto determine the AoA. Ambiguities, such as cos(x)=cos(−x) are resolvedby rotating the DPA.

In another simple embodiment, the antenna-system is comprised of a DPAplus one or more additional antennas such that it has at least threeports. The isolation element is comprised of a tuned filter or areceiver at each port where all the receivers are coherent. The additionof at least one more port allows the SoI levels from the DPA ports to beestimated using a coherent process. The coherent SoI level estimation isdone by correlating each DPA port output SoI with the SoI from one ormore of the additional ports or a weighted sum from other ports. Thecorrelation process can be done over a period of time that is eithercontinuous or not continuous as will be described in greater detaillater in this document.

In another simple embodiment, the antenna-system has four ports and iscomprised a set of two DPAs oriented orthogonally to each other, such asnorth-south and east-west, or a QPA. This embodiment, with both DPAsoriented for vertical polarization, would be appropriate forapplications needing to find the AoA (or line of bearing relative tonorth) of a vertical ground-wave and where the antenna array is fixedand cannot be rotated. By having these four ports, calculations can bedone to make the RF emitter sensing system immune to not only its ownnoise, but also homogeneous noise in the atmosphere picked up by theantennas. With both DPA antennas oriented for vertical polarization andlooking for a ground-wave signal, both DPAs are working on an H-planepattern, as described in Equation 3 in paragraph [00125]. For thisvertical ground-wave case, or application, we will represent the azimuthangle, where φ=0° is east and φ=90° is north. With this definition, thevoltage out versus angle patterns for the four ports are:

W _(N) _(V) ∝(1+sin φ)/2

W _(S) _(V) ∝(1−sin φ)/2

W _(E) _(V) ∝(1+cos φ)/2

W _(W) _(V) ∝(1−cos φ)/2  (4)

Quad-Port PxMA Antenna (QPA)

Rather than using a pair of DPAs that are oriented orthogonally to eachother, another four-port embodiment could use a QPA, which is a pair oforthogonal DPAs sharing the same conductive surfaces. FIG. 6 is amechanical drawing showing a QPA that is nominally spherical. Like theDPAs of FIG. 3 and FIG. 5, it has a top conductor 605 and a bottomconductor 610, and has the original two ports, or port-pair, port-1 andport-2, and coaxial cables 325 and 330, but now also has an additionalsecond set of ports, or port-pair, port-3 and port-4, and coaxial cables625 and 630. In this case the first pair of ports produce cardioidpatterns aimed 0 and 180 degrees, while the additional pair of ports(port-3 and port-4) produce cardioid patterns aimed 90 and 270 degrees.Each port-pair form, with the conductive surfaces, a loop, where the twoloops are orthogonal to each other. The new second magnetic dipolemoment {right arrow over (m)}₂ for the port-3 port-4 pair is orthogonalto the first magnetic dipole moment {right arrow over (m)}₁ from theport-1 port-2 pair. As with all PxMA elements, the height, and width,and length, and termination impedances are generally setup so {rightarrow over (m)}₁=c{right arrow over (p)} and {right arrow over(m)}₂=c{right arrow over (p)} to obtain their unique symmetric cardioidpattern at arbitrarily low frequency performance with a resistivetermination and no additional calibration.

Symbol 655 is a schematic symbol intended to pictorially represent 4orthogonal ports with polarization and directionality consistent withthe QPA or a pair of similarly oriented DPA antennas.

FIG. 7 is a mechanical drawing for an alternative embodiment of a QPAconstructed almost identically as the spherical QPA, with a topconductive surface 705, a bottom conductive surface 710, and the sameport connections as FIG. 6, but is cubical instead of spherical.

FIGS. 6 and 7 show balanced versions of a QPA. Unbalanced versions canbe built by replacing the lower conductor 610 or 710 with a conductorthat is wide, much like that shown in FIG. 4. In this case, the lowerconductor is typically either a square, with a width that is on theorder of 3 times or more the height of the sphere (FIG. 6) or cube (FIG.7), or round with a diameter that is on the order of 3 times or more theheight of the sphere or cube versions.

HPA and DHPA Hex Port Antenna and Dual Hex Port Antenna

Another embodiment useful for ultra-miniature 3D and fully polarimetricDF applications is an antenna system that includes one or more HPA orDHPA elements. FIG. 19A is a mechanical drawing showing an HPA and FIG.19B is a mechanical drawing showing a DHPA. Rather than using threeseparate DPAs that are oriented orthogonally to each other, an HPA isthree orthogonal DPAs that share a common volume. Similarly, rather thanusing three separate QPAs that are oriented orthogonally to each other,a DHPA is three orthogonal QPAs that share a common volume. As shown inFIGS. 19A and 19B, both the HPA and DHPA are made with three pairs ofconductive surfaces. Pair-1 is comprised of surface 1 a, and surface 1b. Pair-2 is comprised of surface 2 a and 2 b. Pair-3 is comprised ofsurface 3 a and 3 b. Here, the numbers 1, 2, and 3 refer to opposingface-pairs (i.e. faces on opposite sides of cube 4 in FIGS. 19A and 19B)and where the letters a and b refer to a specific face in the face-pair.These conductive surfaces are shown as squares plus wires but could takeon other shapes such as a circular or even a complex shape like ajig-saw like piece.

Each face-pair, or pair of conductive surfaces, connect to either twoports, if the conductive surface pair are connected as a DPA, or connectto four ports if the conductive surface pair are connected as a QPA.Face-pair 1 (i.e. 1 a and 1 b in FIGS. 19A and 19B) has ports 11, 12when connected as a DPA, and also has ports 13, and 14 when connected asa QPA. Face-pair 2 (i.e. 2 a and 2 b) has ports 21, 22 when connected asa DPA, and also has ports 23, and 24 when connected as a QPA. Face-pair3 (i.e. 3 a and 3 b) has ports 31, 32 when connected as a DPA and alsohas ports 33, and 34 when connected as a QPA. Each port, or feed point,has a two terminals (e.g., + and −) that connect to their respectiveconductive surface. For clarity, the connection at the feed is shownbeing made through a pair of “wires” having equal length. These “wires”are, however, simply part of the conductive surfaces and can be shaped,such as in a triangular sheet. Port 11 connects through the pair ofwires where the first wire in the pair is 1 a 1 (going to face 1 a) andthe second wire in the pair is 1 b 1 (going to face 1 b). Port 12connects through the pair of wires 1 a 2 (going to face 1 a) and 1 b 2(going to face 1 b). Port 13 connects through the pair of wires 1 a 3(going to face 1 a) and 1 b 3 (going to face 1 b). Port 14 connectsthrough the pair of wires 1 a 4 (going to face 1 a) and 1 b 4 (going toface 1 b). Face 1 a plus wires 1 a 1, 1 a 2, 1 a 3, 1 a 4 form aconductive surface. Face 1 b plus wires 1 b 1, 1 b 2, 1 b 3, and 1 b 4form another conductive surface. These two conductive surfaces and fourports form a first QPA. Port-11 and port-12 form a port-pair, andport-13 and port-14 form a port pair such that the port-pairs areorthogonal to each other. Each port-pair can be connected to twinlead ora balun transformer or 180-degree splitter or hybrid. A connection ofthis type is illustrated in FIG. 3. Instead of wires, the conductivesurface can be shaped and bent, or be comprised of bonded pieces toprovide these connections, such as using triangular wedges similar tothose of FIG. 7 instead of wires.

A second QPA orthogonal to the first QPA is constructed similarly. Port21 connects through the pair of wires 2 a 1 (going to face 2 a) and 2 b1 (going to face 2 b). Port 22 connects through the pair of wires 2 a 2(going to face 2 a) and 2 b 2 (going to face 2 b). Port 23 connectsthrough the pair of wires 2 a 3 (going to face 2 a) and 2 b 3 (going toface 2 b). Port 24 connects through the pair of wires 2 a 4 (going toface 2 a) and 2 b 4 (going to face 2 b). These four ports are equivalentto a second QPA, that is orthogonal to the first QPA, where port-21 andport-22 form a port-pair, and port-23 and port-24 form a port pair wherethe port-pairs are orthogonal to each other.

A third QPA orthogonal to both the first and second QPAs is constructedsimilarly. Port 31 connects through the pair of wires 3 a 1 (going toface 3 a) and 3 b 1 (going to face 3 b). Port 32 connects through thepair of wires 3 a 2 (going to face 3 a) and 3 b 2 (going to face 3 b).Port 33 connects through the pair of wires 3 a 3 (going to face 3 a) and3 b 3 (going to face 3 b). Port 34 connects through the pair of wires 3a 4 (going to face 3 a) and 3 b 4 (going to face 3 b). Port-31 andport-32 form a port-pair, and port-33 and port-34 form a port pair wherethese port-pairs are orthogonal to each other.

It can be seen that the DHPA shown in FIG. 19B is a super set of theHPA, QPA, and DPA. It is a PxMA antenna where all elements share acommon volume, and that can be easily reduced to a fully polarimetricHPA simply by eliminating 6 of the ports, such as eliminating 13, 14,23, 24, 33, and 34, as shown in FIG. 19A. It can be reduced to a QPA byremoving all but one surface-pair. The QPA can be reduced to a DPA byremoving one port-pair from the QPA. Thus it is seen that manycombinations of reductions of the DHPA can be used according the needsof particular applications.

Exemplary Antenna Array Embodiments

More complex embodiments can use an antenna-system with more ports tooffer more degrees of freedom to (1) cover more polarizations, (2)estimate and remove atmospheric noise of different polarizations, (3)combine multiple elements with amplitude and phase weights to aim nullsand/or beams in desired directions, and (4) provide ports that areshadowed from wavefronts from particular directions. For example, FIG.12 shows an embodiment that includes an antenna-system with sixteenports. It uses top and side view symbols from FIGS. 3 (350 and 355) andFIG. 6 (655) to convey the different 3D orientations making up theantenna system. The sixteen ports allow the RF emitter sensing system tooperate against a conductive plane such as an aircraft wing, or theearth, and estimate the polarization as well as the angle-of-arrival inmultipath conditions multipath conditions such as with waves that bounceoff of the ionosphere and ground. Operating in this multipathenvironment is important in many applications, such as innear-vertical-incidence-skywave (NVIS) operations.

The minimum antenna-system that can provide all three H-field axes andall three E-field axes is a set where the three DPA loops are orientedorthogonally and the three DPA heights are oriented orthogonally, suchas Pε{N_(V), S_(V), E_(H), W_(H), U_(E), D_(E)}, or Pε{E_(V), W_(V),N_(H), S_(H), U_(N), D_(N)}, each with six ports. The HPA can beoriented to provide either of these. The DHPA provides both. Theaddition of other orientations and positions and shadowed elementsallows additional degrees of freedom useful for things such asestimating polarization, self calibration, mitigating bias terms fromnoise, and separately estimating a desired AoA from multiple wavefrontsat the same frequency, such as multipath.

Shielding/Shadowing

One key feature in an embodiment using an antenna-system of FIG. 12 isthe inclusion of shadowed ports. Generally, to achieve a desired beampattern capable of isolating multipath terms at low frequencies from anarray of elements requires large spacing between elements. In order toisolate multipath and still have a miniature size, the two far right DPAelements in FIGS. 12, 1205 and 1206, are shadowed (or shielded in adirection), so that they pick up vertically polarized ground-wavesignals, but have reduced sensitivity to signals coming down from thesky.

Previously we defined port nomenclature to be Pε{N_(V), S_(V), E_(V),W_(W)} respectively referring to north, south, east, west, andvertically polarized, Pε{N_(H), S_(H), E_(H), W_(H)} respectivelyreferring to north, south, east, west, and horizontally polarized, andPε{U_(N), D_(N), U_(E), D_(E)} respectively referring to up-north,(sensitive to waves polarized with their E-field oriented north-southcoming down from the sky), down-north (sensitive to waves polarized withtheir E-field oriented north-south coming from up the ground), up-east(sensitive to an east-west polarized wave coming from the sky),down-east (sensitive to an east-west polarized wave coming from theground). To account for ports connected to shadowed elements, we willappend these with an S subscript to denote a port that is shadowed. Forexample, Pε{N_(VS), S_(VS), E_(VS), W_(VS)} respectively refers tonorth, south, east, west, and vertically polarized, and shadowed ports.

FIG. 8 shows a balanced DPA 805 with its top covered by an absorbing andor reflective layer 870, which shields or shadows the antenna. Since theshield 870 is small relative to the wavelength, it works by creating ashort depth shadow. Because the DPA 805 is thin, it can be placed closeenough to shield 870 to fall within the shadow. Typically, the absorbingcover 870 is placed three or more antenna mid-line heights above the topantenna conductor 305. In alternate embodiments, the DPA could also be aQPA, HPA, or DHPA. An antenna mid-line height is the distance betweenthe conductors 305 or 310 and the symmetry plane between them. In orderto have equal shielding capability, the size of shield layer 870 mustincrease as the spacing from the antenna to 870 increases. The layer 870perimeter distance around the antenna 880 is typically at least the sumof two antenna mid-line heights plus the spacing to 870.

FIG. 9 shows a balanced DPA 805 that is covered by absorbing and/orreflective layers 870 and 970, both above it (upper reflective layer870) and below it (lower reflective layer 970). Like the upper layer870, the spacing from the lower antenna conductor 310 to the lowerabsorbing layer 970 is three or more antenna mid-line heights. Thisstructure is particularly beneficial for an embodiment in which theantenna is elevated, and where it must isolate a sky-wave coming downfrom the sky, and a ground-bounce wave coming up from the ground, fromthe desired wave propagating parallel to the ground. The sky-wave comingdown and would normally couple to both ports. The reflection of the skywave off of the ground would also couple into both ports. By placing thethin absorptive reflective material above and below the DPA such thatthe DPA is in the close-up shadow of the absorptive reflective material,the wave propagating parallel to the ground comes into the antennaunimpeded, while the sky-wave is reduced enough to enhance the accuracyof the AoA estimate. The antenna could be any miniature antenna, such asa QPA, HPA, or DHPA. The absorptive reflective material can be made oftypical RF materials like or metal, or mu-metal, or foam/sheetscontaining lossy carbon powder or fibers.

FIG. 10 shows an unbalanced DPA 1005 with its top covered by anabsorbing and/or reflective layer 870. Again, layer 870 is spaced threeunbalanced antenna heights above the top antenna conductor 305, and thelayer 870 perimeter distance around the antenna 880 should be at leastthe sum of two antenna mid-line heights plus the spacing to layer 870.

FIG. 13 shows an embodiment with an antenna-system 101B including 18ports, where four QPAs provide sixteen ports and the remaining two portsare vertical and horizontal omni-directional antennas. Isolation element102A is shown with a switch network 1305 and a calibration signalgenerator 1315 that allow calibration signals to flow through the QPAelements into the receivers, or directly into the receivers. Theseconnections allow the signal path from the antennas, through thereceivers 1310 in the isolation element 102A, to the estimator element103A, to be measured so that signal level comparisons are not changeddue to different receiver paths having different gains. It also confirmsall wiring.

FIG. 14 shows a low cost embodiment in which the antenna-system 101C has14 ports, but the isolation element 102B has only two coherent receivers1410. In this case, a switch network 1405 allows one antenna to feedboth receivers 1410, for calibration purposes, and allows any antenna toconnect to either receiver. By connecting the same antenna port to bothreceivers 1410, any difference between them can be measured andeliminated. In the embodiment of FIG. 13, the SoI from all antenna portswas provided to the estimation element 103B simultaneously. But in theembodiment of FIG. 14, each port is isolated and provided sequentiallyto the processor 1420 in the measurement element 103B. This sequentialembodiment works well for signals that use a constant envelopmodulation, such as frequency modulation (FM), linear frequencymodulation (LFM), bi-phase shift keying (BPSK) and quadrature phaseshift keying (QPSK). For example, most VHF/UHF handheld radios use FMmodulation. The two ports that are subtracted in the estimator element103B are switched immediately near the antenna, such as the N_(V) andS_(V) ports, so that the exact same wiring and receiver is used. In thisway, nothing can effect or bias this difference calculation.

Isolation Element

In applications where it is known that the SoI will always besignificantly larger than any other signal, the isolation element 102Bcould simply be a wire that passes the SoI to the output. It could alsosimply amplify the SoI and pass it to the output. It could also performfrequency translation. For example, the center frequency of the SoIcould be translated so that the output was an intermediate frequency(IF). It could also be translated to DC and the output for each antennaport could be delivered as a complex pair of signals, i.e. an in-phaseand quadrature (I/Q) pair of signals. The receivers 1310 in FIG. 13 andthe receivers 1410 in FIG. 14 would receive tuning commands from theestimator element (1320 and 1420 respectively) to set the centerfrequency and bandwidth and modulation type and possibly the listentimes. These receivers would also pass any blanking times to theestimator element's processor 1320 and 1420 so that it could properlywork with the isolated SoI.

In most applications, the SoI is accompanied by other signals. For theseapplications the isolation element 102B would pass the signal from eachantenna-system port through a filtering process to isolate the SoI fromall the other signals. This filtering process can happen in both thefrequency domain and time domain. In the simplest case, a frequencydomain filter would remove signals at different frequencies, while thetime domain filter would remove bursts of interference, or would removenoise during periods of time when the SoI was off. Alternatively, thefiltering process could operate as a joint-time-frequency process. Forexample, an SoI that was repetitively ramping in frequency, such as aradar chirp, could be match filtered (i.e. compressed) to create ahigh-SNR isolated SoI. The isolation element 102B could include ananalog-to-digital converter that delivers digital samples of the SoI ata series of time points. In this case, all or part of the filteringprocess could take place digitally. Numerous well known digital signalprocessing (DSP) techniques can be applied to isolate the SoI, such asforward inverse Fourier and Laplace transforms, finite and infiniteimpulse response (FIR and IIR) filters, joint time frequency analysis(JTFA), MUSIC (multiple signal classification), stretch processing,singular value decomposition (SVD), etc.

Estimator Element

The estimator element 1320, 1420 starts by estimating the level of theSoI at each of the ports. Estimating the level can use an incoherent orcoherent mechanism. For example, squaring the voltage on a port,averaging the squared value for some period of time, and taking a squareroot of the average (the square root of the mean of the square, or RMS)is the classic mechanism and is incoherent. This incoherent function canbe accomplished in many ways, such as with a square-law diode detectordriving a capacitor, or a bolometer, or it could be done digitally afterthe signal is digitized using an analog-to-digital converter.

One embodiment uses a coherent mechanism to estimate the level of theSoI. The signal from one port, containing the SoI plus noise, ismultiplied by the signal from another port, which also contains the SoIbut has a different noise composition. The product is then averaged overa period of time. This function can be accomplished either digitally, orwith analog hardware such as by using log, anti-log, integration, andsummation functions.

An incoherent estimator element can be as simple as a digital or analogmultimeter, a table, and a process that an operator follows. In thiscase the process is that the operator connects the multimeter to eachoutput port of the isolation element and records the multimeter's RMSvoltage reading for each port. The operator then finds the row in thetable that most closely matches the set of multimeter readings, andreads the AoA that is listed for that row. This process could add steps,such as the operator performing some calculations using the measuredvalues, and then finding the row in the table that most closely matchesthe set of results from the calculations, and reading the AoA that islisted for that row. Or the operator could perform a set of calculationsthat directly produced the AoA.

More typically, the estimator element contains a processor that takes inthe SoI outputs from the isolation element and generates an estimate ofthe AoA. This could be an analog processor or a digital processor or acombination of both. For example, the estimator element could includenon-linear network diodes and a processor for performing analog log andexponential and summation functions that takes in the SoI measured atthe various antenna ports by the isolation element, and outputs an AoA.Alternatively, the estimator element could be a digital process thatcould operate via a process similar to the process the operator used inthe example case above. It could also use a process for determining thelevel of the SoI at each port that was coherent and immune to noise inthe RF emitter sensing system and immune to homogeneous noise picked upby the antennas. Regardless of implementation (e.g. digital or analog),the estimator element implements a formula, or function F({ν_(P)}|_(∀P))that produces an AoA estimate given all the signals output by theisolation element.

Some applications benefit from knowing the confidence level in aparticular AoA estimate. By evaluating the variance of the SoI outputsover time, the estimator can also output a confidence level for the AoAestimate it provides.

Non-Coherent Method of Estimating AoA

The estimator element typically starts by estimating the RMS voltagelevel of the SoI at each port. The RMS voltage is measured over a timeinterval of interest centered at time t with a duration of T. Equation 5shows the calculation for an arbitrary DPA where its two ports are aimedin opposite directions, and written as (P=N) and (P=S) for north andsouth for clarity:

$\begin{matrix}{{{D_{N}\left( {t,T} \right)} = {\sqrt{\frac{1}{T}{\int_{t - \frac{T}{2}}^{t + \frac{T}{2}}{{v_{N}^{2}(\tau)}{\tau}}}}\mspace{14mu} {and}}}{{D_{S}\left( {t,T} \right)} = \sqrt{\frac{1}{T}{\int_{t - \frac{T}{2}}^{t + \frac{T}{2}}{{v_{S}^{2}(\tau)}{\tau}}}}}} & (5)\end{matrix}$

Recall that φ=0 is due east and φ=90 due north. A north-south-orientedDPA's symmetry about the north-south axis running between its two portsmeans that a signal coming from φ=90−x (or north−x) degrees and a signalcoming from φ=90+x (or north+x) degrees will generate an identical ratioin power levels between its two ports. Similarly a signal coming xdegrees above or below the horizontal plane will generate an identicalratio in power levels at the two ports.

For a north-south oriented DPA that is vertically polarized, a portratio function R_(NV)(D_(N),D_(S)) has been defined, where the NVsubscript refers to North, and Vertical polarization, and where thearguments D_(N) and D_(S) are understood to be ports aimed in oppositedirections (i.e. north and south) and vertically polarized to match theV subscript on the R_(NV). The port ratio function R_(NV)(D_(N),D_(S))varies monotonically between +1 and −1 for a signal coming from φ=90 to90 degrees (north to south) respectively, and that is zero at φ=0 and180 (east and west), as follows:

$\begin{matrix}{{R_{NV}\left( {D_{N},D_{S}} \right)} = {{\frac{2\; D_{N}}{D_{N} + D_{S}} - 1} = {\frac{D_{N} - D_{S}}{D_{N} + D_{S}} = {1 - {\frac{2\; D_{S}}{D_{N} + D_{S}}.}}}}} & (6)\end{matrix}$

Following the same construction pattern, R_(EV)(D_(E),D_(W)), for aneast-west oriented and vertically polarized DPA, and R_(UN)(D_(U),D_(D))for an up-down oriented DPA polarized with its E-field oriented north,are:

$\begin{matrix}{{{R_{EV}\left( {D_{E},D_{W}} \right)} = {{\frac{2\; D_{E}}{D_{E} + D_{W}} - 1} = {\frac{D_{E} - D_{W}}{D_{E} + D_{W}} = {1 - \frac{2\; D_{W}}{D_{E} + D_{W}}}}}},{and}} & (7) \\{\mspace{79mu} {{R_{UN}\left( {D_{U},D_{D}} \right)} = {{\frac{2\; D_{U}}{D_{U} + D_{D}} - 1} = {\frac{D_{U} - D_{D}}{D_{U} + D_{D}} = {1 - {\frac{2\; D_{D}}{D_{U} + D_{D}}.}}}}}} & (8)\end{matrix}$

For a signal in any plane containing its two ports, R variesmonotonically between +1 and −1 for a signal coming from φ=0 to 180degrees respectively (e.g. east to west in a horizontal plane). R iszero at φ=90 and −90 degrees (north and south). The up-down orientedantenna follows the same pattern with R_(UN) varying monotonicallybetween +1 and −1 for a signal coming down from the sky, to a signalcoming up from the ground, respectively, and zero for a signal comingfrom the horizon.

The functions R_(NV), R_(EV), and R_(UN) are useful for four reasons.First, since the quantity is based on a ratio, the output is independentof the amplitude of the SoI. Similarly, if the power is scaled at eachport by the same value, the ratio does not change. Such a scaling isequivalent to multiplying both the numerator and denominator by the samevalue. This feature is important for using the coherent power estimationmethod described later. Second, the output of either port of the DPA cango to zero without a divide by zero issue. Third, if the antennasgenerate the ideal beam patterns, such as shown in Equation 1 or thesimplified ones shown in Equation 4, inverting these functions can bedone mathematically in closed form. Fourth, the inversion function issmooth and can easily be shaped to be correct for the actual antennapatterns, such as when they are disturbed by local objects, as opposedto the ideal patterns.

The closed form solution is found as follows:

$\begin{matrix}{{{R_{N\; V}(\varphi)} = {\frac{\left( \frac{1 + {\sin \; \varphi}}{2} \right) - \left( \frac{1 - {\sin \; \varphi}}{2} \right)}{\left( \frac{1 + {\sin \; \varphi}}{2} \right) + \left( \frac{1 - {\sin \; \varphi}}{2} \right)} = {\sin \; \varphi}}},} & (9) \\{{\varphi = {\sin^{- 1}\left( {R_{N\; V}(\varphi)} \right)}},} & (10)\end{matrix}$

or combining Equation 10 with Equation 6:

$\begin{matrix}{\hat{\varphi} = {{\sin^{- 1}\left( \frac{D_{N} - D_{S}}{D_{N} + D_{S}} \right)}.}} & (11)\end{matrix}$

Recall that the estimator element implements a function F({ν_(P)}|_(∀P))that produces an AoA estimate given all the signals output by theisolation element. In this simplest case, with only a single DPA, thesignal processor implements a function F that generates an estimated AoAin an arbitrarily-oriented plane containing the two ports of the DPA,from the received signals, i.e. {circumflex over (φ)}=F(ν_(N)(t),ν_(S)(t)). In this case, the function F uses Equations 5 and thenEquation 11 to estimate the AoA.

In alternate embodiments, instead of using an inverse sine (i.e.arcsine) to determine the AoA (i.e. {circumflex over (φ)}), a lookuptable could be used. Such a table could deviate from an inverse cosineto correct for other factors, such as local reflections, and therebyenhance the accuracy of {circumflex over (φ)}.

This single DPA embodiment is useful when it is known that targets canonly appear in a sector on one side of the DPA and in a known planecontaining the two DPA ports. For example, when it is know that the SoIwill always be within +/−50 degrees of east and on the ground (i.e. atan elevation angle of zero), then a single north-south oriented DPA isthe simplest embodiment.

Since the DPA pattern is symmetric about its axis, the ports on anorth-south oriented DPA respond identically to an incident fieldx-degrees east and x-degrees west relative to north. This ambiguity isresolved by either a priori knowledge, turning the antenna and takingmultiple measurements, or by having additional antenna ports that allowthe correct side to be determined. The additional antenna ports could beanother DPA that is orthogonally oriented (in this case, orientedeast-west) Similarly, a QPA or 12-PA could be used, as they provide theports necessary to resolve the ambiguity inherent in a simple pair ofports. With a pair of DPAs or a QPA, the function {circumflex over(φ)}=F({ν_(P)}|_(∀P)) becomes {circumflex over (φ)}=F(ν_(N)(t),ν_(S)(t), ν_(E)(t), ν_(W)(t)) and can be computed as:

$\begin{matrix}{\hat{\varphi} = \left\{ {\begin{matrix}{\sin^{- 1}\left( {R_{N\; V}(\varphi)} \right)} & {{\left. \begin{matrix}{{{when}\mspace{14mu} D_{S}} > {{D_{N}\mspace{14mu} {and}}\mspace{14mu} - 90} \leq \varphi \leq 0} \\{{{when}\mspace{14mu} D_{N}} > {D_{S}\mspace{14mu} {and}\mspace{14mu} 0} \leq \varphi \leq 90}\end{matrix} \right\} D_{E}} > D_{W}} \\{180 - {\sin^{- 1}\left( {R_{N\; V}(\varphi)} \right)}} & {{\left. \begin{matrix}{{{when}\mspace{14mu} D_{N}} > {D_{S}\mspace{14mu} {and}\mspace{14mu} 90} \leq \varphi \leq 180} \\{{{when}\mspace{14mu} D_{S}} > {D_{N}\mspace{14mu} {and}\mspace{14mu} 180} \leq \varphi \leq 270}\end{matrix} \right\} D_{W}} > D_{E}}\end{matrix},} \right.} & (12)\end{matrix}$

or as:

$\begin{matrix}{\hat{\varphi} = \left\{ {\begin{matrix}{\cos^{- 1}\left( {R_{E\; V}(\varphi)} \right)} & {{\left. \begin{matrix}{{{when}\mspace{14mu} D_{E}} > {D_{W}\mspace{14mu} {and}\mspace{14mu} 0} \leq \varphi \leq 90} \\{{{when}\mspace{14mu} D_{W}} > {D_{E}\mspace{14mu} {and}\mspace{14mu} 90} \leq \varphi \leq 180}\end{matrix} \right\} D_{N}} > D_{S}} \\{- {\cos^{- 1}\left( {R_{E\; V}(\varphi)} \right)}} & {{\left. \begin{matrix}{{{when}\mspace{14mu} D_{W}} > {{D_{E}\mspace{14mu} {and}}\mspace{14mu} - 180} \leq \varphi \leq {- 90}} \\{{{when}\mspace{14mu} D_{E}} > {{D_{W}\mspace{14mu} {and}}\mspace{14mu} - 90} \leq \varphi \leq 0}\end{matrix} \right\} D_{S}} > D_{N}}\end{matrix},} \right.} & (13)\end{matrix}$

or as:

$\begin{matrix}{{\hat{\varphi} = {{{arc}\; {\tan \left( \frac{R_{N\; V}}{R_{E\; V}} \right)}} = {{a\; \tan \; 2\left( {R_{E\; V},R_{N\; V}} \right)} = {a\; \tan \; 2\left( {\frac{D_{E} - D_{W}}{D_{E} + D_{W}},\frac{D_{N} - D_{S}}{D_{N} + D_{S}}} \right)}}}},} & (14)\end{matrix}$

where a tan 2 is the standard 4-quadrant arc-tangent function built intomany computer languages such as Fortran, Matlab, and Mathcad.

Compute and Table Methods to Generate an AoA Estimate

The function F can be made many ways depending on the needs of theapplication. For minimum complexity, it can be made with a lookup table.For example, suppose the antenna system uses three orthogonal QPAs. Inthis case, (R_(NV), R_(EV)), (R_(EH),R_(UN)), and (R_(NH), R_(UE))should be measured. These six terms are simply extensions obtained byrotating the polarization of the R_(NV), R_(EV), or R_(UN) functionsshown in Equations 6, 7, and 8. Relative to an axis of the antennasystem, the lookup table could list in its first three columnsrespectively, an azimuthal angle, an elevation angle, and a polarizationangle. Corresponding to these angles, in the remaining columns, it couldlist any number of expected measurement metrics derived from the portsin the antenna system. For example, six ratio measures (e.g. {tilde over(R)}_(NV) {tilde over (R)}_(EV) {tilde over (R)}_(EH) {tilde over(R)}_(UN) {tilde over (R)}_(NH) {tilde over (R)}_(UE)—one for each portpair), or the sums and differences they are based on, or the port SoIlevels, could be placed in columns four and up in the table. Here, thesuperscript ˜ in the {tilde over (R)}_(NV), {tilde over (R)}_(EV), etc.indicates it is a value that is expected based on a calibration. Thecalibration would measure theses values for emitters at known angles andpolarizations. Calibration measurements incorporate disturbances fromobjects near the antenna system, allowing the RF emitter sensing systemto be accurate even with those disturbances. By virtue of thesecalibration values, the table captures an accurate mapping betweenmeasured values, and estimated angles (azimuth, elevation, andpolarization) associated with the SoI.

The RF emitter sensing system measures the SoI from the twelve portsassociated with the three QPAs, and in some disclosed embodimentsapplies corrections to mitigate construction tolerances, appliescorrections to mitigate homogeneous environmental noise, and therebygenerates a set of calibrated measurements (R_(NV), R_(EV)), (R_(EH),R_(UN)) and (R_(NH), R_(UE)).

For each row in the table, the processor computes an error-value ε suchas:

ε=({tilde over (R)} _(NV) −R _(NV))²+({tilde over (R)} _(H) −R_(EH))²+({tilde over (R)} _(UE) −R _(UE))²+({tilde over (R)} _(NH) −R_(NH))²+({tilde over (R)} _(EV) −R _(EV))²+({tilde over (R)} _(UN) −R_(UN))²,

or:

$ɛ = {{{{a\; \tan \mspace{14mu} 2\left( {{\overset{\sim}{R}}_{EV},{\overset{\sim}{R}}_{N\; V}} \right)} - {a\; \tan \mspace{14mu} 2\left( {R_{E\; V},R_{N\; V}} \right)}}} + {{{a\; \tan \mspace{14mu} 2\left( {{\overset{\sim}{R}}_{E\; H},{\overset{\sim}{R}}_{U\; N}} \right)} - {a\; \tan \mspace{14mu} 2\left( {R_{E\; H},R_{U\; N}} \right)}}} + {{{{a\; \tan \mspace{14mu} 2\left( {{\overset{\sim}{R}}_{N\; H},{\overset{\sim}{R}}_{U\; E}} \right)} - {a\; \tan \mspace{14mu} 2\left( {R_{N\; H},R_{U\; E}} \right)}}}.}}$

Given this error metric, the processor, or an operator, would find therow having the minimum error ε, and the estimates for the azimuth,elevation, and polarization would be provided in the first three columnsof that row. For some applications, in particular environments wheresignificant anomalies occur, additional parameters, such as

${1 - \frac{D_{E\; V} + D_{W\; V}}{D_{N\; V} + D_{S\; V}}},{{{and}\mspace{14mu} 1} - {\frac{D_{U\; E} + D_{D\; E}}{D_{N\; H} + D_{S\; H}}\mspace{14mu} {and}\mspace{14mu} 1} - \frac{D_{U\; N} - D_{D\; N}}{D_{E\; H} + D_{W\; H}}}$

can be used. By determining whether or not they are close to zero, orsignificantly above or below zero the system can use these values tomodify the equations or table columns used for estimation, or to alertthe operator that less trust should be placed on the output.

Alternatively, in certain angular ranges, the values placed in the firstthree columns can be “special numbers” that indicate that a particularalternative table be used. It can sometimes be advantageous to havemultiple tables, with particular tables designed for particular angularranges. Having multiple tables can reduce memory requirements andfacilitate usage of different error function formulations in differentangular ranges such as error functions that use different portcombinations or metrics for different angular ranges. These features canmakes them useful for antenna systems with a large number of ports, orwhere special rules are needed to mitigate ambiguities in particularangular ranges—for example, ambiguities caused by interference fromlocal objects. If desired, one could break down the angle space into anarbitrary number of pieces so a different curve or equation could beused for each one.

An equation-based approach can easily be substituted for the abovetable-based implementation by using standard curve fitting methods. Eachoutput angle in a table, can use an interpolating curve fitting functionto allow the angle to be found directly from the set of parameters usedin the table.

Discontinuous Integration

The integration duration shown in Equation 5 covers a single contiguousinterval and is appropriate for many applications. In otherapplications, such as when the signal sometimes disappears or is blankedto avoid a burst of interference, an alternative embodiment couldperform this integral incrementally over a plurality of time segmentsthat may not be contiguous with each other. An example is shown inEquation 15, where there are J time-segments:

Let Pε{the ports in the antenna system, e.g. NV, SV, EV, WV, NH, DH, UE,DE, etc.}Let jε{1, 2, . . . J}Let iε{1, 2, . . . J}Let ψ_(i)={(t_(ai),t_(bi))} where (t_(ai),t_(bi)) are start and stoptimes, if discrete, start and stop indexesLet T_(i)=t_(bi)−t_(ai) where this is the time interval, if discrete,the number of sample intervals

${{Let}\mspace{14mu} \tau_{j}} = {\sum\limits_{i = 1}^{j}\; T_{i}}$

If continuous, use the integrals below, if discrete, use the summationsbelow:

$\begin{matrix}\begin{matrix}{{{Let}\mspace{14mu} {\beta_{i,P}\left( \psi_{i} \right)}} = {\int_{t_{ai}}^{t_{bi}}{{v_{P}^{2}(\tau)}\ {\tau}\mspace{14mu} {or}}}} \\{= {\frac{{v^{2}\left( t_{bi} \right)} + {v^{2}\left( t_{ai} \right)}}{2} + {\sum\limits_{k = 1}^{T_{i} - 1}\; {v_{P}^{2}\left( {t_{ai} + k} \right)}}}}\end{matrix} & (15) \\{{{Let}\mspace{14mu} {D_{P}\left( \tau_{j} \right)}} = {\frac{1}{\tau_{j}}{\sum\limits_{i = 1}^{j}\; {\beta_{i,P}\left( \psi_{i} \right)}}}} & \; \\\begin{matrix}{{{Let}\mspace{14mu} {\beta_{i,j,P}^{\prime}\left( \psi_{i} \right)}} = {\int_{t_{ai}}^{t_{bi}}{\left( {{v_{P}(\tau)} - D_{j,P}} \right)^{2}\ {\tau}\mspace{14mu} {or}}}} \\{= {\frac{\left( {{v\left( t_{bi} \right)} - D_{j,P}} \right)^{2} + \left( {{v\left( t_{ai} \right)} - D_{j,P}} \right)^{2}}{2} +}} \\{{\sum\limits_{k = 1}^{T_{i} - 1}\; \left( {{v_{P}\left( {t_{ai} + k} \right)} - D_{j,P}} \right)^{2}}}\end{matrix} & \; \\{{{Let}\mspace{14mu} {\sigma_{P}^{2}\left( \tau_{j} \right)}} = {\frac{1}{\tau_{j}}{\sum\limits_{i = 1}^{j}\; {\beta_{i,j,P}^{\prime}\left( \psi_{i} \right)}}}} & \;\end{matrix}$

where the set ψ of J arbitrary time intervals allows the integration toskip increments of time that are advantageous to skip. For example, attimes with high interference, it can be advantageous to effectively“blank” and not use the received signal. In fact, the isolation elementmight blank the signal in such circumstances. In this case, part of itsoutput would inform the estimation element when the SoI is blanked sothat the estimator could respond appropriately. Equation 15 is shownbroken down to highlight how the processor can incrementally integratethe SoI over J different time intervals defined by ψ. If further showsthe computation of an incremental estimate of the variance σ² at thei^(th) step. When the signal is digitized and known at discrete pointsin time, the summation formulations can be used rather than thecontinuous time integrals that are useful for analog forms ofprocessing.

In some embodiments, the integration times can be adaptive, such asresponding to blanking intervals caused by adaptive blankers that may beoperating in the isolation element. For other applications, anembodiment may set the integration time to a fixed value at the factory.Other applications prefer an embodiment that allows the integration timeto be set by the operator.

Alternatively, to provide a desired variance level corresponding to adesired AoA estimation accuracy, an embodiment can track the variance asthe integration proceeds and automatically adjust the total integrationinterval. For example, the variance can be compared to a threshold suchthat the next increment in J only occurs if the variance is too high.

Coherent Unbiased Method of Estimating AoA

In practice, the voltages at the output of the receiver are corrupted bynoise. Breaking out the SoI and noise terms separately, the estimatedSoI power level from Equation 5 becomes:

$\begin{matrix}{{{D_{N}\left( {t,T} \right)} = {{\frac{1}{T}{\int_{t - \frac{T}{2}}^{t + \frac{T}{2}}{\left( {{v_{{SoI}_{N}}(\tau)} + {n_{N}(\tau)}} \right)^{2}\ {\tau}\mspace{14mu} {and}\mspace{14mu} {D_{S}\left( {t,T} \right)}}}} = {\frac{1}{T}{\int_{t - \frac{T}{2}}^{t + \frac{T}{2}}{\left( {{v_{{SoI}_{S}}(\tau)} + {n_{S}(\tau)}} \right)^{2}\ {{\tau}\;.}}}}}}{\mspace{11mu} \mspace{11mu}}} & (16)\end{matrix}$

Since (ν_(SoI) _(N) (τ)+n_(N)(τ))²=(ν_(SoI) _(N) ²(τ)+2ν_(SoI) _(N)(τ)n_(N)(τ)+n_(N) ² (τ)) and E└∫2ν_(SoI) _(N) (τ)┘=0, equation 16becomes

$\begin{matrix}{{{D_{N}\left( {t,T} \right)} = {{\frac{1}{T}{\int_{t - \frac{T}{2}}^{t + \frac{T}{2}}{\left( {{v_{{SoI}_{N}}^{2}(\tau)} + {n_{N}^{2}(\tau)}} \right)\ {\tau}\mspace{14mu} {and}\mspace{14mu} {D_{S}\left( {t,T} \right)}}}} = {\frac{1}{T}{\int_{t - \frac{T}{2}}^{t + \frac{T}{2}}{\left( {{v_{{SoI}_{S}}^{2}(\tau)} + {n_{S}^{2}(\tau)}} \right)\ {{\tau}\;.}}}}}}{\mspace{11mu} \mspace{11mu}}} & (17)\end{matrix}$

It is clear from Equation 17 that each result is biased by its squarednoise term. Therefore, this non-coherent embodiment works best when theSoI level is much higher than the receiver and background noise level.Clearly it would be desirable to eliminate this bias.

A slightly more complex embodiment uses a minimum of three antenna portsand a coherent-SoI-estimation method. In this case, one or more of theports serves as a coherent reference containing the SoI. The coherentreference voltage is notated as ν_(R)(t). Both ports of any particularDPA are correlated with a common reference that is independent from thatDPA.

There are multiple ways to create an effective ν_(R)(t) In someembodiments, for any set of antenna ports available to use as areference, the port with the strongest SoI is used. For applicationsneeding the lowest complexity, this single port reference embodiment isoften preferred. For higher accuracy, at the expense of complexity,multiple ports can be combined to produce a reference with a highersignal-to-noise ratio (SNR). Multiple combining methods that tradeperformance for complexity exist in the literature. For example, onepreferred embodiment applies classic maximum ratio combining (MRC)across the set of ports available for use as a reference.

The core principle is that the coherent-SoI-estimation method estimatesthe RMS SoI level at each port without the above noise bias term, andthereby improves the accuracy of the AoA estimate.

The coherent-energy-estimation method estimates the SoI power levelusing coherent integration as follows:

$\begin{matrix}{{D_{N}\left( {t,T} \right)} = {{\frac{1}{T}{\int_{t - \frac{T}{2}}^{t + \frac{T}{2}}{{v_{N}(\tau)}{v_{R}(\tau)}\ {\tau}\mspace{14mu} {and}\mspace{14mu} {D_{S}\left( {t,T} \right)}}}} = {\frac{1}{T}{\int_{t - \frac{T}{2}}^{t + \frac{T}{2}}{{v_{S}(\tau)}{v_{R}(\tau)}{{\tau}\;.}}}}}} & (18)\end{matrix}$

For clarity, sometimes two subscripts are used on the D metric so thatboth the port being measured (the first subscript) and the port used asthe reference (the second subscript) are identified by the respectivesubscripts. In this case, Equation 18 is written as:

$\begin{matrix}{{D_{N\; R}\left( {t,T} \right)} = {{\frac{1}{T}{\int_{t\frac{T}{2}}^{t + \frac{T}{2}}{{v_{N}(\tau)}{v_{R}(\tau)}\ {\tau}\mspace{14mu} {and}\mspace{14mu} {D_{S\; R}\left( {t,T} \right)}}}} = {\frac{1}{T}{\int_{t - \frac{T}{2}}^{t + \frac{T}{2}}{{v_{S}(\tau)}{v_{R}(\tau)}{{\tau}\;.}}}}}} & (19)\end{matrix}$

Expanding to show the noise terms produces:

$\begin{matrix}\begin{matrix}{{{v_{N}(\tau)}{v_{R}(\tau)}} = {\left( {{v_{{SoI}_{N}}(\tau)} + {n_{N}(\tau)}} \right)\left( {{v_{{SoI}_{R}}(\tau)} + {n_{R}(\tau)}} \right)}} \\{= {{{v_{{SoI}_{N}}(\tau)}{v_{{SoI}_{R}}(\tau)}} + {{v_{{SoI}_{N}}(\tau)}{n_{R}(\tau)}} +}} \\{{{{v_{{SoI}_{R}}(\tau)}{n_{N}(\tau)}} + {{n_{N}(\tau)}{{n_{R}(\tau)}.}}}}\end{matrix} & (20)\end{matrix}$

where ν_(SoI) _(N) (τ) is the SoI component of the port-N receiveroutput voltage, n_(N)(τ) is the noise component of the port-N receiveroutput voltage, ν_(SoI) _(N) (τ) and n_(R)(τ) are the SoI and noisecomponents, respectively, of the reference (port-R) representing eithera receiver output voltage, or a combination of port voltages.

Assuming the noise component is the receiver noise and not atmosphericnoise, the expected values for the integration of all the cross termsare zero, i.e.:

E└∫ν _(SoI) _(N) (τ)n _(R)(τ)dτ┘=0, E└∫ν _(SoI) _(R) (τ)n _(N)(τ)dτ┘=0,and E└∫n _(N)(τ)n _(R)(τ)dτ┘=0  (21)

the SoI RMS level estimates become:

$\begin{matrix}{{{D_{NR}\left( {t,T} \right)} = {\frac{1}{T}{\int_{t - \frac{T}{2}}^{t + \frac{T}{2}}{{v_{{SoI}_{N}}(\tau)}{v_{{SoI}_{r}}(\tau)}{\tau}\mspace{14mu} {and}}}}}{{D_{SR}\left( {t,T} \right)} = {\frac{1}{T}{\int_{t - \frac{T}{2}}^{t + \frac{T}{2}}{{v_{{SoI}_{S}}(\tau)}{v_{{SoI}_{R}}(\tau)}{\tau}}}}}} & (22)\end{matrix}$

showing that an SoI power measure is provided with no bias from receivernoise.

By incorporating this coherent integration method, an embodiment canobtain accurate AoA estimates on a signal so small that it is below thenoise floor of a receiver optimized to demodulate the signal. This“sensitivity below the noise floor” feature is important for manyapplications. It allows a small portable radio with its inherently smallinsensitive antennas to be hand carried around to search for a signalthat, while large enough to interfere with a sensitive system using alarge well placed antenna, is too small for the RF emitter sensingsystem to demodulate and “hear” the information, such as music, speech,or data.

For clarity, an example of using MRC (maximum ratio combining) on twoports to provide a higher SNR reference signal follows. Suppose the RFemitter sensing system uses a north/south oriented DPA (DPA_(NS)) and aneast/west oriented DPA (DPA_(EW)). Equation 22 is used to compute allthe cross correlations, D_(NE), D_(SE), D_(NW), D_(SW). We find themaximum magnitude of these and identify which term it is, so suppose|D_(NE)|=max(|D_(NE)|, |D_(SE)|, |D_(NW)|, |D_(SW)|). This outcome wouldmean, for a single port reference, we would use the E port as thereference for the DPA_(NS), and we would use the N port as the referencefor the DPA_(EW). Instead, we can combine the E and W ports to make abetter SNR reference to use with DPA_(NS), and similarly combine the Nand S ports to make a better reference to use with the DPA_(EW). Sincethe integration in Equation 22 is communicative, we can combine theterms used in the reference signal before or after the integration. Wewill take advantage of this fact and perform the combination afterintegration. Note also that D_(XY)=D_(YX). The combining may be done byweighting and summing the port voltages, or by weighting and summing theE and H field components.

The process for using the port voltages directly starts with creatingthe weighted sum. Using DPA_(NS) as the source of the reference signal,we have

D _(ER) =a·D _(EN) +b·D _(ES), and

D _(WR) =a·D _(WN) +b·D _(WS)  (23)

and we need to find the weights a and b. When |D_(EN)|>|D_(ES)| thenormalized weights for MRC are a=D_(EN) ²/(D_(EN) ²+D_(ES)²),b=D_(EN)·D_(ES)/(D_(EN) ²+D_(ES) ²). Since scaling is not importantin this application, the computation can be simplified to a=1,b=D_(ES)D_(EN) or a=D_(EN), b=D_(ES). When |D_(ES)|>|D_(EN)| the weights for MRCare the normalized weights for MRC are a=D_(EN)·D_(ES)/(D_(ES) ²−D_(ES)²), b=D_(ES) ²/(D_(EN)+D_(ES) ²). Again, since scaling is not importantin this application, this computation can be simplified toa=D_(EN)/D_(ER), b=1 or a=D_(EN), b=D_(ER). The a and b weights areapplied to Equation 23 to generate the higher SNR D_(ER), and D_(WR)terms used in finding the AoA. This same process is followed to computeD_(NR), and D_(SR) with DPA_(EW) providing the reference signal. Whileillustrating the process for two ports for clarity, MRC allows anynumber of ports to be combined to improve the SNR and one skilled in theart should be able to apply MRC weighting to any number of ports.

Given the same scenario with D_(NE) the largest term, the process forweighting and combining the EM field components starts by separating theEM components. Again, starting with DPA_(NS) to supply the referencesignal, and using the East port DPA_(EW) since it produced the highestmagnitude, the E-field term is e_(ENS)=(D_(NE)+D_(SE))/2 and the H-fieldterm is h_(ENS)=(D_(NE)−D_(SE))/2. We want to weight and recombine theseas

D _(ER) =a(D _(NE) +D _(SE))/2+b(D _(NE) −D _(SE))/2=a·e _(ENS) ±b·h_(ENS), and

D _(WR) =a(D _(NW) +D _(SW))/2+b(D _(NW) −D _(SW))/2.  (24)

When |e_(ENS)|>|h_(ENS)|, the simplified un-normalized weights for MRCare a=1, b=h_(ENS)/e_(ENS). When |h_(ENS)|>|e_(ENS)|, the simplifiedun-normalized weights for MRC are a=e_(ENS)/h_(ENS), b=1. With thesecoefficients established for DPA_(NS), the a and b weights are appliedto Equation 24 to generate the higher SNR D_(ER), and D_(WR) terms usedin finding the AoA. This same process is followed to compute D_(NR), andD_(SR) with the ports of DPA_(EW) combined to provide the referencesignal. While illustrating the process for two ports for clarity, MRCallows any number of ports to be combined to improve the SNR and oneskilled in the art should be able to extend the application of MRCweighting to any number of ports.

Discontinuous Coherent Integration

The coherent integration shown in Equation 22 can use a non-continuousset of time intervals that follows the same outline as used in Equation5, but with a coherent, instead of incoherent, integrand, as shown inEquation 15.

Let Pε{the ports in the antenna system}Let jε{1, 2, . . . J}Let iε{1, 2, . . . J}Let ψ_(i)={(t_(ai), t_(bi))} where (t_(ai), t_(bi)) are start & stoptimes, or if discrete, start & stop indexesLet T_(i)=t_(bi)−t_(ai)=the time interval, or if discrete, the number ofsample intervals

${{Let}\mspace{14mu} \tau_{j}} = {\sum\limits_{i = 1}^{j}T_{i}}$

If continuous, use the integral, if discrete, use the summation:

$\begin{matrix}{{Let}\mspace{14mu} \begin{matrix}{{\beta_{i,P}\left( \psi_{i} \right)} = {\int_{t_{ai}}^{t_{bi}}{{v_{P}(\tau)}{v_{R}(\tau)}{\tau}\mspace{14mu} {or}}}} \\{= {\frac{{{v_{P}\left( t_{bi} \right)}{v_{R}\left( t_{bi} \right)}} + {{v_{P}\left( t_{ai} \right)}{v_{R}\left( t_{ai} \right)}}}{2} +}} \\{{\sum\limits_{k = 1}^{T_{i} - 1}{{v_{P}\left( {t_{ai} + k} \right)}{v_{R}\left( {t_{ai} + k} \right)}}}}\end{matrix}} & (25) \\{{{Let}\mspace{14mu} {D_{P}\left( \tau_{j} \right)}} = \left( {\frac{1}{\tau_{j}}{\sum\limits_{i = 1}^{j}{\beta_{i,P}\left( \psi_{i} \right)}}} \right)^{2}} & \; \\{{Let}\mspace{14mu} \begin{matrix}{{\beta_{i,j,P}^{\prime}\left( \psi_{i} \right)} = {\int_{t_{ai}}^{t_{bi}}{\left( {{{v_{P}(\tau)}{v_{R}(\tau)}} - \sqrt{D_{P}\left( \tau_{j} \right)}} \right)^{2}\mspace{14mu} {or}}}} \\{= {\frac{\begin{matrix}{\left( {{{v_{P}\left( t_{bi} \right)}{v_{R}\left( t_{bi} \right)}} - \sqrt{D_{P}\left( \tau_{j} \right)}} \right)^{2} +} \\\left( {{{v_{P}\left( t_{ai} \right)}{v_{R}\left( t_{ai} \right)}} - \sqrt{D_{P}\left( \tau_{j} \right)}} \right)^{2}\end{matrix}}{2} +}} \\{{\sum\limits_{k = 1}^{T_{i} - 1}\left( {{{v_{P}\left( {t_{ai} + k} \right)}{v_{R}\left( {t_{ai} + k} \right)}} - \sqrt{D_{P}\left( \tau_{j} \right)}} \right)^{2}}}\end{matrix}} & \; \\{{{Let}\mspace{14mu} {\sigma_{P}^{2}\left( \tau_{j} \right)}} = {\frac{1}{\tau_{j}}{\sum\limits_{i = 1}^{j}{\beta_{i,j,P}^{\prime}\left( \psi_{i} \right)}}}} & \;\end{matrix}$

where the set ψ, contains J arbitrary time intervals, allowing theintegration to skip increments of time that are advantageous to skip. Itfurther shows the computation of an incremental estimate of the varianceσ_(J) ² at the j^(th) step. When the signal is digitized and known atdiscrete points in time, the summation formulations are used rather thanthe continuous time integrals that are useful for analog forms ofprocessing.

A signal processor in the estimator element implements a function F thatincludes this additional reference signal so that {circumflex over(φ)}=F_(φ)(ν_(N)(t), ν_(S)(t), ν_(R)(t)) and {circumflex over(θ)}=F_(θ)(ν_(N)(t), ν_(S)(t), ν_(R)(t)). Some embodiments of functionF, which provide the best sensitivity and accuracy, use thiscoherent-energy-estimation method to make the AoA estimate unbiased toreceiver noise.

A similar embodiment uses the same three antenna ports but the isolationelement only has two channels and uses switches to connect twoantenna-system ports at a time to the two channels. In this case, whileone channel isolates the SoI in the reference signal, the other channelis switched to alternately isolate the SoI in the north or the SoI inthe south port. In this case, ν_(N)ν_(R) is measured in one timeinterval and ν_(S)ν_(R) is measured in an alternate time interval. Aslong as the RMS SoI level remains fixed in the alternate intervals, theAoA estimate is the same. This two-receiver embodiment is preferred whenlow power is a high priority and the SoI meets this “fixed level acrossalternate intervals” requirement. FM and digital signals typically workwell with this embodiment. FIG. 14 uses this two-receiver technique tocover a 14 port antenna-system.

Starting with the embodiment where the antenna-system is a single DPA, aslightly more complex embodiment adds a second DPA that is nominallyoriented orthogonally to the first DPA. For example, if the first DPAwas north-south oriented, this second DPA would be nominally east-westor up-down oriented. Together, the two DPAs provide the RF emittersensing system with 4 ports aimed nominally every 90 degrees, forexample, north, east, south and west (N, E, S, W, or 90, 0, −90, and 180degrees), where ν_(N)(t), ν_(S)(t), ν _(E)(t), ν_(W)(t) are the voltagesat the output of the isolation element connected to the antenna-system'snorth, south, east, and west ports respectively.

Removing Homogeneous Sky and Atmospheric Noise Using an Extra Port

Assuming that there is homogeneous atmospheric and sky and backgroundnoise being picked up by the antennas, and that this noise hashomogeneous coherence from port to port, then there is an additionalnoise term, which can be called (t). In other words, Equation 22 wouldbecome:

$\begin{matrix}{\mspace{20mu} {{{D_{NR}\left( {t,T} \right)} = {\frac{1}{T}{\int_{t - \frac{T}{2}}^{t + \frac{T}{2}}{\left( {{v_{{SoI}_{N}}(\tau)} + n_{{sky}_{N}}} \right)\left( {{v_{{SoI}_{R}}(\tau)} + n_{{sky}_{R}}} \right){\tau}}}}}{{D_{NR}\left( {t,T} \right)} = {{{\frac{1}{T}{\int_{t - \frac{T}{2}}^{t + \frac{T}{2}}{{v_{{SoI}_{N}}(\tau)}{v_{{SoI}_{R}}(\tau)}{\tau}}}} + {\frac{1}{T}{\int_{t - \frac{T}{2}}^{t + \frac{T}{2}}{{n_{{sky}_{N}}(\tau)}{n_{{sky}_{R}}(\tau)}{\tau}}}}} = {{{s_{N}s_{R}} + {n_{{sky}_{N}}n_{{sky}_{R}}}} = {{s_{N}s_{R}} + n_{sky}^{2}}}}}}} & (26)\end{matrix}$

where s_(N) and s_(R) are the RMS voltage levels of the SoI at the N andR ports.

In this case, assuming that the E-port SoI is stronger than the W-port,so that the E-port is used for the reference, R_(NV) becomes:

$\begin{matrix}{R_{NV} = {\frac{D_{NE} - D_{SE}}{D_{NE} + D_{SE}} = {\frac{\left( {{s_{N}s_{E}} + n_{sky}^{2}} \right) - \left( {{s_{S}s_{E}} + n_{sky}^{2}} \right)}{\left( {{s_{N}s_{E}} + n_{sky}^{2}} \right) + \left( {{s_{S}s_{E}} + n_{sky}^{2}} \right)} = {\frac{{s_{N}s_{E}} - {s_{S}s_{E}}}{{s_{N}s_{E}} + {s_{S}s_{E}} + {2n_{sky}^{2}}} = {\frac{s_{N}\left( {s_{E} - s_{S}} \right)}{{s_{E}\left( {s_{N} + s_{S}} \right)} + {2n_{{sky}\;}^{2}}}.}}}}} & (27)\end{matrix}$

Similarly, if the N port is used for the reference, R_(EW) becomes:

$\begin{matrix}{R_{EV} = {\frac{D_{EN} - D_{WN}}{D_{EN} + D_{WN}} = {\frac{\left( {{s_{E}s_{W}} + n_{sky}^{2}} \right) - \left( {{s_{W}s_{N}} + n_{sky}^{2}} \right)}{\left( {{s_{E}s_{W}} + n_{sky}^{2}} \right) + \left( {{s_{W}s_{N}} + n_{sky}^{2}} \right)} = {\frac{{s_{E}s_{N}} - {s_{W}s_{N}}}{{s_{E}s_{N}} + {s_{W}s_{N}} + {2n_{sky}^{2}}} = {\frac{s_{N}\left( {s_{E} - s_{W}} \right)}{{s_{N}\left( {s_{E} + s_{W}} \right)} + {2n_{sky}^{2}}}.}}}}} & (28)\end{matrix}$

As long as the sky-noise term is relatively small, relative to the SoI,the reference signal cancels.

In addition to eliminating AoA estimation bias due to noise in thereceivers, it would be advantageous to also remove AoA estimation biasdue to homogeneous noise picked up by the antennas. Some embodiments dothis as follows.

In an embodiment with at least one more port, any four ports can use thefifth port as the coherent reference for the four ports. When used thisway the sky-noise term cancels in the argument for the arctangentfunction, and the AoA estimate becomes unbiased relative to homogeneousnoise. This fact is illustrated, or explained by example, as follows.Substituting a common reference channel in the construction of Equations27 and 28, causes them to become:

$\begin{matrix}{{R_{NV} = {\frac{D_{NR} - D_{SR}}{D_{NR} + D_{SR}} = {\frac{\left( {{s_{N}s_{R}} + n_{sky}^{2}} \right) - \left( {{s_{S}s_{R}} + n_{sky}^{2}} \right)}{\left( {{s_{N}s_{R}} + n_{sky}^{2}} \right) + \left( {{s_{S}s_{R}} + n_{sky}^{2}} \right)} = {\frac{{s_{N}s_{R}} - {s_{S}s_{R}}}{{s_{N}s_{R}} + {s_{S}s_{R}} + {2n_{sky}^{2}}} = \frac{s_{R}\left( {s_{N} - s_{S}} \right)}{{s_{R}\left( {s_{N} + s_{S}} \right)} + {2n_{{sky}\;}^{2}}}}}}},} & (29)\end{matrix}$

and:

$\begin{matrix}{{R_{EV} = {\frac{D_{ER} - D_{WR}}{D_{ER} + D_{WR}} = {\frac{\left( {{s_{E}s_{R}} + n_{sky}^{2}} \right) - \left( {{s_{W}s_{R}} + n_{sky}^{2}} \right)}{\left( {{s_{E}s_{R}} + n_{sky}^{2}} \right) + \left( {{s_{W}s_{R}} + n_{sky}^{2}} \right)} = {\frac{{s_{E}s_{R}} - {s_{W}s_{R}}}{{s_{E}s_{R}} + {s_{W}s_{R}} + {2n_{sky}^{2}}} = \frac{s_{R}\left( {s_{E} - s_{W}} \right)}{{s_{R}\left( {s_{E} + s_{W}} \right)} + {2n_{sky}^{2}}}}}}},} & (30)\end{matrix}$

and the arctangent argument becomes:

$\begin{matrix}{{\frac{R_{NV}}{R_{EV}} = {{\frac{s_{R}\left( {s_{N} - s_{S}} \right)}{s_{R}\left( {s_{E} - s_{W}} \right)}\frac{{s_{R}\left( {s_{E} + s_{W}} \right)} + {2n_{sky}^{2}}}{{s_{R}\left( {s_{N} + s_{S}} \right)} + {2n_{sky}^{2}}}} = {\frac{s_{R}\left( {s_{N} - s_{S}} \right)}{s_{R}\left( {s_{E} - s_{W}} \right)} = \frac{s_{N} - s_{S}}{s_{E} - s_{W}}}}},} & (31)\end{matrix}$

because s_(N)+s_(S)=s_(E)+s_(W) since s_(N)+s_(S) and s_(E)+s_(W) arethe same E-field.Removing Homogeneous Sky and Atmospheric Noise without an Extra PortRemoving Homogeneous Sky and Atmospheric Noise without an Extra Port

In an embodiment with just the four ports, it is still possible togenerate an AoA estimate that is unbiased to homogeneous noise asfollows. Since sin² x+cos² x=1 the preferred embodiment estimates thesky noise term 2n_(sky) ², by using a function ξ=Φ(A,B,C,D) that solves:

$\begin{matrix}{{\left( \frac{D_{NE} - D_{SE}}{D_{NE} + D_{SE} - \xi} \right)^{2} + \left( \frac{D_{EN} - D_{WN}}{D_{EN} + D_{WN} - \xi} \right)^{2}} = {{\left( \frac{A}{\left. {B - \xi} \right)} \right)^{2} + \left( \frac{C}{D - \xi} \right)^{2}} = 1}} & (32)\end{matrix}$

where A=D_(NE)−D_(SE), B=D_(NE)+D_(SE), C=D_(EN)−D_(WN), andD=D_(EN)+D_(WN).

One solution for the function Φ(A,B,C,D) is:

$\begin{matrix}{{{\Phi \left( {A,B,C,D} \right)} = {{Re}\left\lbrack {\frac{B}{2} + \frac{D}{2} - \sqrt{\frac{F}{6} + \frac{H}{4} + \frac{I}{144}} - \sqrt{\frac{F}{3} - \frac{H}{4} - \frac{I}{144} - \frac{3E}{\sqrt{{I + {36H} + {24F}}\;}}}} \right\rbrack}},} & (33)\end{matrix}$

where:

$\mspace{20mu} {{E = {{A^{2}B} - {BC}^{2} - {A^{2}D} + {C^{2}D}}},\mspace{20mu} {F = {A^{2} + {B^{2}/2} - {BD} + C^{2} + {D^{2}/2}}},\mspace{20mu} {G = {\left( {B - D} \right)^{2}\left( {{4A^{2}} - B^{2} + {2{BD}} + {4C^{2}} - D^{2}} \right)}},{H = \sqrt[\frac{1}{3}]{\begin{matrix}{{\sqrt{3\left( {{432E^{4}} - {64E^{2}F^{3}} + {G\left( {{16F^{4}} - {144E^{2}F}} \right)} + {8F^{2}G^{2}} + G^{3}} \right)}/72} +} \\{{E^{2}/2} - {F^{3}/27} + {{G\left( {{2{BD}} - {2A^{2}} - B^{2} - {2C^{2}} - D^{2}} \right)}/24}}\end{matrix}}},\mspace{20mu} {and}}$$\mspace{20mu} {I = \left\{ {\begin{matrix}{\left( {{4F^{2}} - {3G}} \right)/H} & {{{if}\mspace{14mu} H} \neq 0} \\0 & {{{if}\mspace{14mu} H} = 0}\end{matrix}.} \right.}$

Given the solution ξ=Φ(A,B,C,D) in Equation 33, substituting forEquations 27 and 28 produces the following:

$\begin{matrix}{{R_{NV} = {\frac{A}{B - \xi} = {\frac{D_{NE} - D_{SE}}{D_{NE} + D_{SE} - \xi} = {\frac{s_{E}\left( {s_{N} - s_{S}} \right)}{{s_{E}\left( {s_{N} + s_{S}} \right)} + {2n_{sky}^{2}} - \xi} = {\frac{s_{E}\left( {s_{N} - s_{S}} \right)}{s_{E}\left( {s_{N} + s_{S}} \right)} = \frac{s_{N} - s_{S}}{s_{N} + s_{S}}}}}}},} & (34)\end{matrix}$

and:

$\begin{matrix}{{R_{EV} = {\frac{C}{D - \xi} = {\frac{D_{EN} - D_{WN}}{D_{EN} + D_{WN} - \xi} = {\frac{s_{N}\left( {s_{E} - s_{W}} \right)}{{s_{N}\left( {s_{E} + s_{W}} \right)} + {2n_{sky}^{2}} - \xi} = {\frac{s_{N}\left( {s_{E} - s_{W}} \right)}{s_{N}\left( {s_{E} + s_{W}} \right)} = \frac{s_{E} - s_{W}}{s_{E} + s_{W}}}}}}},} & (35)\end{matrix}$

and the function F to estimate the AoA, in the preferred embodiment,becomes

$\begin{matrix}{\hat{\varphi} = {{F\left( {{v_{N}(t)},{v_{S}(t)},{v_{E}(t)},{v_{W}(t)}} \right)} = {{\arctan \left( \frac{R_{NV}}{R_{EV}} \right)} = {{atan}\; 2{\left( {R_{EV},R_{NV}} \right).}}}}} & (36)\end{matrix}$

In this embodiment, R_(NV) and R_(EV) from Equations 34 and 35 havetaken advantage of (a) coherent integration to eliminate bias fromself-noise and allow long integration times with high gain on the SNR,(b) a function Φ(A,B,C,D) to remove homogeneous noise picked up by theantennas, and (c) a ratio-based function, in this case an arctangent, toprovide an AoA estimate that is unbiased with respect to both the noisein the receiver as well as the homogeneous noise picked up by theantennas. Since the reference signal cancels in the ratio, the beampattern of the reference also cancels, and all that is left is thedesired SoI sum and difference ratio. Since this ratio is independent ofthe SoI power level, an accurate angle estimate is provided that isrobust to signal level changes.

In order to correct for anomalies caused by local objects that scatterthe incoming wave, instead of using the a tan 2 function, the function Fcould be configured to also use an approximation to the arcsine ofR_(NS), the arccosine of R_(EW), and/or lookup tables, as discussedabove, based on calibration measurements. In this way, enhanced accuracycan be achieved even in the context of anomalies.

This method of removing homogeneous noise can be applied to other setsof antennas that can be combined to generate four orthogonal (e.g. 0,90, 180, 270 degrees) unidirectional beams with a pattern that isnominally a raised cosine function. For example, take a first case wherethe output of a dipole and a loop are properly scaled so they can besummed to produce a first output that is unidirectional, and subtractedto produce a second output that is unidirectional, where the two beamsaim in opposite directions. With a second loop oriented 90 degreesrelative to the first loop, another beam-pair of oppositely aimed beamscould be made that are orthogonal to the first beam-pair. Similarly,take a second case where a pair of dipoles is combined to produce afirst output that is unidirectional, and a second output that isunidirectional, where the two beams aim in opposite directions. For thiscase, to illustrated, assume a pair of dipoles or a pair of loopsdisplaced along the x-axis at (x,y) of (−λ/20,0), and (λ/20,0). Thesignal on (−λ/20,0) could be delayed by λ/10 and subtracted from thesignal at (λ/20,0) to create a first pattern with a null in the −xdirection and a beam in the +x direction. The signal on (λ/20,0) couldbe delayed by λ/10 and subtracted from the signal at (λ/20,0) to createa second pattern with a null in the +x direction and a beam in the −xdirection. By adding another set of antennas displaced along the y-axis,at (0,−λ/20), and (0,λ/20) and doing a similar combinations, anotherbeam-pair can be made in the +y and −y direction-orthogonal to the firstbeam-pair. In both the first case and the second case, the sameprocedure can be used to find and use a function to estimate thehomogeneous noise being picked up by the set of antennas and remove itsaffect.

Correcting for Non-Ideal Cardioid

The previous equations were idealized and assumed a perfectback-to-front ratio of zero. Due to finite construction tolerances, anyelement's size, shape, position, and termination network impedance, andloss, for either a PxMA element, or a loop and dipole combination, therealized front-to-back ratio is typically not perfect. In practice,however, the estimator element can incorporate a correction for thisnon-ideal back-to-front ratio, thus mitigating its deleterious effect.An important feature of this calibration is that it allows thetermination impedance on the PxMA elements such as the DPA, QPA, HPA,and DHPA to drive amplifiers and circuits that may not be ideal, yetstill provide high directivity to arbitrarily low frequency. The antennapattern can be corrected by measuring and estimating the back-to-frontratio term ε(λ) during calibration, and using this term duringoperations to remove the error. In this case, the measured patterns arebecome:

$\begin{matrix}{{v_{N} = {a\; \frac{1 + {\left( {1 - {2{ɛ(\lambda)}}} \right)\cos \; \varphi}}{2}}},{{{and}\mspace{14mu} v_{S}} = {a\; {\frac{1 - {\left( {1 - {2{ɛ(\lambda)}}} \right)\cos \; \varphi}}{2}.}}}} & (37)\end{matrix}$

Based on measured antenna patterns for these two ports, a curve fit isperformed to estimate the ε(λ) term, calling it {circumflex over(ε)}(λ). The sign of ε(λ) is negative if the back-lobe voltage isinverted relative to the boresight voltage. FIG. 16 illustratesmagnitude patterns when ε(λ) is positive, negative, or ideal. Given{circumflex over (ε)}(λ), a correction factor

${k(\lambda)} = \frac{1}{\left( {1 - {2{\hat{ɛ}(\lambda)}}} \right)}$

is computed. This correction factor can be determined at the time ofmanufacture or in the field after measuring the antenna pattern.

This correction factor can be applied to the antenna outputs but is moretypically applied to the output of the isolation element. Theapplication is done as follows. For each DPA, the sum of the portvoltages provides a measure of just the electric field componentν_(NSE). (This electric field component would simply be the dipole portvoltage if a loop and a dipole were used to sense the EM field.):

$\begin{matrix}{v_{NSE} = {{v_{N} + v_{S}} = {{a\left( {\frac{1 + {\left( {1 - {2{ɛ(\lambda)}}} \right)\cos \; \varphi}}{2} + \frac{1 - {\left( {1 - {2{ɛ(\lambda)}}} \right)\cos \; \varphi}}{2}} \right)} = {a.}}}} & (38)\end{matrix}$

The difference of the port voltages provides a measure of the magneticfield component (which would simply be the loop's port voltage if adipole and loop were used to sense the EM field), where the normalizedmagnetic field component ν_(NSM) is:

$\begin{matrix}{v_{NSM} = {\frac{v_{N} - v_{S}}{v_{N} + v_{S}} = {{{a\left( {\frac{1 + {\left( {1 - {2{ɛ(\lambda)}}} \right)\cos \; \varphi}}{2} - \frac{1 - {\left( {1 - {2{ɛ(\lambda)}}} \right)\cos \; \varphi}}{2}} \right)}/v_{NSE}} = {\left( {1 - {2{ɛ(\lambda)}}} \right)\cos \; {\varphi.}}}}} & (39)\end{matrix}$

Equation 38 mathematically shows the result of applying the correctionfactor to the normalized magnetic term and recombining it with thenormalized electric field component, which is 1:

$\begin{matrix}{{{\hat{v}}_{N} = {\frac{1 + {{k(\lambda)}v_{NSM}}}{2} = {\frac{1 + {\frac{\left( {1 - {2{ɛ(\lambda)}}} \right)}{\left( {1 - {2{\hat{ɛ}(\lambda)}}} \right)}\cos \; \varphi}}{2} = \frac{1 + {\cos \; \varphi}}{2}}}}{{\hat{v}}_{S} = {\frac{1 - {{k(\lambda)}v_{NSM}}}{2} = {\frac{1 - {\frac{\left( {1 - {2{ɛ(\lambda)}}} \right)}{\left( {1 - {2{\hat{ɛ}(\lambda)}}} \right)}\cos \; \varphi}}{2} = {\frac{1 - {\cos \; \varphi}}{2}.}}}}} & (40)\end{matrix}$

Here {circumflex over (ν)}_(N) and {circumflex over (ν)}_(S) are thecorrected voltages for the north and south ports respectively. (If adipole and loop are used to sense the field, {circumflex over (ν)}_(N)and {circumflex over (ν)}_(S) have beam patterns that are aimed northand south respectively. At the north port the recombination is to addthe normalized magnetic term, and at the south port the recombination isto subtract the normalized magnetic term. Assuming the estimated{circumflex over (ε)}(λ) is close to the actual ε(λ), these correctedvoltages will have patterns that are nearly an ideal raised cosine witha null in the backlobe. As such, calculations to find the AoA will be asaccurate as if the antenna and its termination impedances were nearlyideal.

Measured DPA antennas show that this error term is quite small at lowfrequencies and grows at higher frequencies. FIG. 17 shows a plot withoverlaid measurements (dots) and calculated (solid line) curves for theantenna. The agreement over the critical 90 degree sector is quiteremarkable and is always within less than 0.2 dB relative to ideal. FIG.18 plots the error as a function of angle, again highlighting theextremely good match between theory and practice. This low uncorrectederror highlights the highly robust mechanical nature that allows thedescribed RF emitter sensing system embodiment to be extremely small yetachieve high accuracy at arbitrarily low frequencies by incorporatingPxMA elements that remain highly directive at arbitrarily lowfrequencies. The processing disclosed allows elimination of this errorterm.

Taken together, the processing disclosed in the above embodiments of theestimator element allow mitigation of self-noise, homogeneousatmospheric noise, anomalies from local scattering, errors in theantenna construction, as well as mitigation of the small energycollection due to the small size of the antenna so as to provide robustaccuracy and sensitivity that extends below the noise floor of standardreceivers built to demodulate the SoI (signal of interest).

Given the above teaching, it is clear that the invention discloses an RFemitter sensing device wherein the antenna circuit can be configuredsuch that the ports, including those from one or more multiportantennas, can be combined to provide three orthogonal E-field terms andthree orthogonal H-field terms (e.g. E_(X), E_(Y), E_(Z) and H_(X),H_(Y), H_(Z)). The HPA alone provides this capability. Three DPAsconfigured as shown in FIG. 20, also provide this capability. Three QPAsprovide this capability with redundancy that is useful for mitigatingerrors. These terms can take advantage of all of the error mitigationtechniques described above to deliver the best SNR and accuracy. Theestimator is configured to output the three dimensional AoA for each SoIby estimating the three dimensional Poynting vector S of each SoI fromthe antenna circuit's outputs. Typically, the estimator is configured toperform the cross-product, S={right arrow over (E)}×{right arrow over(H)}={right arrow over(x)}(E_(Y)H_(Z)−E_(Z)H_(Y))+ŷ(E_(Z)H_(X)−E_(X)H_(Z))+{circumflex over(z)}(E_(X)H_(Y)−E_(Y)H_(X)) to estimate the Poynting vector. Thiscross-product is illustrated in FIG. 11.

Multipath Immune Field Strength Indicator

Uniquely, at a single point in space, the disclosed RF emitter sensingdevice can measure the separate electromagnetic field components, E_(x),E_(y), E_(z) and H_(x), H_(y), H_(z), for an arbitrarily polarized wavecoming from any direction when it uses an HPA or DHPA. Similarly, whenit uses a QPA, it can measure at a single point in space the separatethree electromagnetic field components, for example, E_(z), H_(x), H_(y)from a vertically polarized wave, coming from any direction. Similarly,when it uses a DPA, it can measure at a single point in space two fieldcomponents, such as E_(z),H_(x), allowing it to sense and isolate theforward wave and reverse wave components aligned with the axis of theDPA. Due to the ability of a DPAs and QPAs to operate at an arbitrarilysmall size, multiple QPAs or DPAs can be placed electrically closetogether such that they measure, at effectively the same point on awavefront, the electromagnetic field components covered by the differentQPAs and/or DPAs. For example, consider a situation where a pair of DPAsare vertically polarized and oriented so they measure E_(z1), H_(x) andE_(z2), H_(y) respectively. In such a case, the closer the DPAs are toeach other, the closer E_(z1) will be to E_(z1). Even if the multipleantennas are not close enough together that E_(z1) and E_(z1) are close,each antenna is still able to sense and isolate the forward wave andreverse wave components aligned with the axes of each loop within theset of multiple antennas. This dual-directional coupling ability tosense and isolate the forward wave and reverse wave components, andhaving access to multiple electromagnetic field components collected inthe exact same point in space gives the disclosed RF emitter sensingsystem the ability to perform better in environments with multipath thanprevious systems where the antennas do not have this ability.

To illustrate the multipath issues, recall how a standing wave is set upin a transmission line. Suppose a transmission line has a short at oneend and an RF signal fed into the other end, and a standing wave isgenerated that is confined to one dimension, down the transmission line.In the transmission line, power flows smoothly in two directions,forward or backward down the transmission line. Note that energy isconserved at all points. The short represents an object causing amultipath reflection. At the short, the two waves (the forward wave andthe backward wave reflected by the short) sum such that the voltage isat a minima (an ideal short would make the voltage zero) and the currentis at a maxima. At a point one quarter wavelength from the short the twowaves sum such that there is a voltage maxima and a current minima.

Expanding this multipath generated standing wave to three dimensions(3D), consider a grass field with a metal building on it. A transmittedwave will travel “forward” and bounce off of the metal building causinga “reflected” or “backward” wave. Just like the transmission line, thetwo waves (forward and reflected) sum such that a standing wave iscreated much like that in transmission line, but now the standing waveis in 3D. The “forward” wave is a spherically expanding wave frontcentered on the transmitter and covering the grass field. The reflected“backward” wave is also spherically expanding from the reflectionsurface. That reflected wave is also covering the grass field. These twowaves cause a two-dimensional spatial standing wave. The E-field mightbe visualized as a waffle, where the height of the waffle isproportional to the E-field. The peaks of the waffle located at thepeaks of the E-field, and the dips in the waffle at nulls of theE-field. The waffle height is high nearby a metal building and lowerfurther from the metal building. The H-field might be visualized asanother waffle, but with its peaks where the E-field waffle is in a dip,and its nulls where the E-field is peaked. The standing wave ratio(VSWR), the maximum voltage to minimum voltage, is highest around themetal building because the forward and reflected waves are of nearlyequal amplitude and therefore can nearly cancel and create deep minima.

In practice, the existence of this standing wave means that when a an RFsensing system operator is standing at one position near the building,the E-field is doubled and at a maxima while the H-field is nearlycanceled and is at a minima. The problem is that when the operator justslightly turns or moves, moving the antennas a few inches, the E-fieldcan change to a minima and the H-field nearly doubled to is a maxima.This is particularly problematic in the VHF and UHF frequency bands.That being the case, any system whose basic operating principle dependson a spatially smooth E-field (i.e. no multipath) such as using a set ofdisplaced dipoles to pick up the E-field at each dipole location, willnot provide robust measurements. It will be confused by the non-smoothbut waffle-like spatially changing E and H fields.

By having access to the various electromagnetic field componentsmeasured at the same point, the disclosed RF emitter sensing device cancalculate a very precise field-strength indicator (FSI) metric that isimmune to multipath. This FSI metric is in stark contrast to what istypically called a received signal strength indicator (RSSI). RSSI isuniversally derived from a single field component—either the E-field(e.g. from a dipole antenna) or the H-field (e.g. from a loopantenna)—on a single channel receiver that has access to only oneantenna port. As a result, RSSI is well known for having an unacceptablyhigh variance in environments with multipath.

Beyond just the FSI versus RSSI benefits, the benefits of this multipathimmunity extends to AoA and range estimation as well. AoA estimationbased on having access to the various electromagnetic field componentsmeasured at the same point in space is in stark contrast to DF-systems,which estimate the AoA based on the phase relationship of the E-fieldsensed by 4-dipoles. These phase relationships are well behaved in ananechoic chamber where only one wavefront exists. But in typical outdoorenvironments with multipath, the multipath sets up standing waves thatcan drastically change the estimated AoA, making it wrong, and making itdrastically change with slight movements in the RF emitter sensingsystem or the target signal. For example, at one location, some of thedipoles might be near an E-field null, while other dipoles are not. At aslightly different location, like moving a few inches with a 450 MHzsignal, the situation could be reversed. As a result, the 4-dipole arrayhas very high sensitivity to multipath. The use of the 4-dipoles assumesa single wavefront with its positionally smooth E and H field. Buthaving a single wavefront is simply not a valid assumption in manyimportant scenarios, like operating in a forest or in an urban areawhere multipath is guaranteed.

A unique property of the disclosed RF emitter sensing device is that itmeasures and isolates the multiple electromagnetic field components allat the exact same spatial location. There are three key factors at work(A) multiple electromagnetic field terms are independently measured, (B)these terms can be calibrated relative to each other, as disclosedabove, and (C) they are measured at the exact same location in space.These three factors combine to allow the disclosed RF emitter sensingdevice to compute a variety of precise field strength indicator (FSI)metrics that are: (1) insensitive to multipath (e.g. the SWR around ametal building, or trees when operating in a forest), and (2)insensitive to operator rotation (i.e. it is omni-directional). Onemetric would be the total field strength. For example, for a verticallypolarized QPA, the total field can be computed as an RSS (root of thesum of the squares) of the electromagnetic field components:

FSI_(V-QPA) _(_) _(total)=√{square root over (E _(Z) ² +H _(X) ² +H _(Y)²)}.  (41)

When the RF emitter sensing device includes an antenna combination thatprovides all electromagnetic field components, the total field can becomputed as RSS of all the components:

FSI_(total)=√{square root over (E _(X) ² +E _(Y) ² +E _(Z) ² +H _(X) ²+H _(Y) ² +H _(Z) ²)}.  (42)

Another metric would be the field strength of just the forward and justthe reflected waves. For example, for a vertically polarized QPA, thesetwo field strengths can be computed as a linear combination of themeasured electromagnetic terms E_(Z) ², H_(X) ², H_(Y) ², as follows:

FSI_(V-QPA) _(_) _(Forward) =E _(Z)+(sin ψ·H _(X)+cos ψ·H _(Y)),and  (43)

FSI_(V-QPA) _(_) _(Reflected) =E _(Z)−(sin ψ·H _(X)+cos ψ·H _(Y)).  (44)

where ψ is used to adjust the weighting on the linearly combined termsand is adjusted to minimize.

$\begin{matrix}{\frac{{FSI}_{V\text{-}{QPA}\; \_ \; {Reflected}}}{{FSI}_{V\text{-}{QPA}\; \_ \; {Forward}}}.} & (45)\end{matrix}$

In this case, the formulation assumes the operator is nominally betweenthe target and the reflector such that the reflected wave is arrivingfrom a direction approximately 180 degrees from the forward wave. Theangle ψ is used to computationally rotate the oppositely aimed cardioidpatterns natively provided by the antenna ports. A DF-system with anantenna configuration that provided all 6 electromagnetic can use asimilar linear combination of all the electromagnetic terms to rotate acardioid pattern in 3D space.

When the disclosed DF-system is built with a pair of DPAs that are closeto each other, a total field FSI can be computed that, while not ideal,is still highly immune to multipath relative to standard RSSI metrics.For example, for a system set up for vertical polarization, the metriccan be computed as the following RSS combination of the measuredelectromagnetic field components:

$\begin{matrix}{{{FSI}_{2\text{-}V\text{-}{DPA}} = \sqrt{\left( \frac{{E_{NS}} + {E_{EW}}}{2} \right)^{2} + H_{NS}^{2} + H_{EW}^{2}}},{or}} & (46) \\{{FSI}_{2\text{-}V\text{-}{DPA}} = \sqrt{\frac{E_{NS}^{2} + E_{EW}^{2}}{2} + H_{NS}^{2} + H_{EW}^{2}}} & (47)\end{matrix}$

The differences between a 4 inch quad port versus a pair of 4 inch DPAsseparated by 4 inches, is likely un-noticeable at HF (3-30 MHz),moderate at VHF (30-300 MHz) where the antenna centers can be as much asabout ⅕th wavelength apart, and significant at UHF (300-1000 MHz) wherethe antenna centers can be as much as about ⅔ wavelength apart.

Based on these teachings it is clear that in addition to the RSS andlinear combinations illustrated, one skilled in the art could use othercombinations of the electromagnetic field components to create fieldstrength indicators optimized for other conditions or to coveradditional polarizations and 3D space.

To be clear, blockages will still affect the FSI. Furthermore, inoutdoor environments these FSI metrics are often still a sum of energiescoming from multiple directions (i.e. there is more than just onereflector), especially in urban environments. So when the operator movesalong a certain bearing, the bearing with the greatest ascent in FSI maynot be toward the target, but some spot midway between the true targetand another reflector. Nonetheless, the slope with operator motion ofthe FSI metrics disclosed are reasonably smooth. They do not bouncearound due to multipath as much as a 4-dipole system does or as much asa typical RSSI does. This fact allows an operator to more quickly closein on a target transmitter based on the FSI.

Ranging

When a DF-operator is gets close to a target (i.e. the “fox” in a radio“fox hunt”) the FSI will be changing quickly with distance to thetarget, since there is a high percentage range-change. This high changerate can provide additional information to zero in on the target, evenin cases where there is lots of multipath and the AoA estimate might notbe as reliable as open areas. Furthermore, the added FSI information isuseful when walking away from a building. In difficult areas, a shortwalk in a few directions can tell you which direction is correct andhelp interpret multiple AoA numbers such as identifying which AoAestimates are likely from reflections and which are likely the target ofinterest.

Uniquely, the disclosed RF emitter sensing device can estimate thetarget range based on one of its unique multipath immune FSI metrics asopposed to triangulation with multiple AoAs measured at differentlocations. The combination of (A) having an FSI that is highly multipathrobust, omnidirectional, and measurable with high accuracy (delta-FSI tohundredths of a dB), (B) having a system that accurately measures itsposition and orientation in real time, and (C) having computationalcapability, allows the disclosed DF-system to estimate the target rangefrom measurements taken at two different ranges.

Using FSI allows an operator the flexibility to move in a straight linetoward a target and still be able to estimate the target range. Thiscapability can be vital when it is desirable to approach the target insecrecy, or where the speed of getting to the target is important. Thisstraight-path capability is in stark contrast to the normal approach ofwalking on a tangential path in order to change the AoA and allowranging by triangulation. It is also in stark contrast to the standardapproach to avoid walking on a tangent path, which is to requiremultiple operators, each with a DF-system, so they can coordinate andjointly triangulate to get a geolocation based on multiple AoA's. Thedisclosed RF emitter sensing device is a single node geolocation systemthat is fast, avoids requiring walking on a tangent path, and becomesmore and more accurate as the operator closes in on a target. Theaddition of the multipath immune FSI functions enables the disclosedDF-system to be a superior single-operator geolocation system.

The equation to solve for range is very simple and requires only twomeasurement points:

PF = Propagation  Factor  ( = 2  for  Free-Space) r = range${{Power}\mspace{14mu} {Received}} \propto \frac{1}{r^{PF}}$$\begin{matrix}{d_{12} = \left( {{distance}\mspace{14mu} {moved}\mspace{14mu} {toward}\mspace{14mu} {the}\mspace{14mu} {target}\mspace{14mu} {between}\mspace{14mu} r_{1}\mspace{14mu} {and}\mspace{14mu} r_{2}} \right)} \\{= {\left( {{distance}\mspace{14mu} {moved}} \right) \cdot {\cos \left( {{AoA} - \left( {{angle}\mspace{14mu} {moved}} \right)} \right)}}}\end{matrix}$${{FSI}_{1} = {\left( \frac{\alpha}{r_{1}} \right)^{{PF}/2} = {{\left( \frac{\alpha}{r_{2} + d_{12}} \right)^{{PF}/2}\mspace{14mu} {and}\mspace{14mu} {FSI}_{2}} = \left( \frac{\alpha}{r_{2}} \right)^{{PF}/2}}}},{\alpha = \frac{{FSI}_{1}^{2/{PF}} \cdot {FSI}_{2}^{2/{PF}} \cdot d_{12}}{{FSI}_{2}^{2/{PF}} - {FSI}_{1}^{2/{PF}}}}$$r_{2} = \frac{{FSI}_{1}^{2/{PF}} \cdot d_{12}}{{FSI}_{1}^{2/{PF}} - {FSI}_{1}^{2/{PF}}}$

where FSI₁ is measured at range r₁, FSI₂ is measured at range r₂, r₂ isdistance d₁₂ closer to the target than range r₁, the units for r₂ arethe same as the units used for d₁₂, α is proportional to the transmittedsignal voltage level emitted from the transmit antenna.

To calibrate, a PF term is entered and adjusted by the operator untilthe correct range is provided for a target at a known range. PF can alsobe found by using multiple points and adjusting it so all measurementpairs give approximately the same geographical position. The operatorcould also enter their geolocation and the RF emitter sensing devicecould lookup the correct PF to use in that particular geographic area.Generally, PF is between 2 and 4, but can occasionally fall outside ofthis range in unusual environments.

This ranging and geolocation capability is especially useful as theoperator closes in on a target since the estimated range becomesextremely accurate and since it gives the operator complete flexibilityon choosing their path to the target.

Operator Display

The disclosed RF emitter sensing device captures more information aboutthe signal than previous DF-systems, and must effectively communicatethis information to the operator. Preferred embodiments communicate tothe operator via one or more of visual, acoustic, vibration, or touchmechanisms according to the particular application's needs. For example,in a portable application, as the system operator walks, displayingimmediate estimates as well as some history of the FSI, the AoAestimates, the AoA variance, and the polarization if available, versustime would also aid the DF-operator in clustering and identifyingbearing and range to participants in a radio net. A user-friendly andeasy to learn display allow the operator to choose settings like historyduration, or dimming rates, or some color-scale encodings. For example,the last N AoA estimates might be shown where:

1) The most recent is bright, and successive older ones are dimmed byage,

2) The dimming rate is slower for AoAs with low variance and faster forAoAs with high variance,

3) The line color is coded by its derivation method—e.g. white for AoAsderived from six ports, red for four ports, and green for AoAs derivedfrom two ports, and

4) Dashed lines are added to show the variance around each line.

Allowing the operator to select line styles and what to display wouldenable experimentation and allow personal customization to suitedifferent personalities or customization for different physicalenvironments—like forest versus city versus relatively open field.

Preferred embodiments would communicate several FSI based metrics, suchas total field, ratio of the reflected field to the forward field, anestimated range based on changes with the field strength versusposition, and an estimated geolocation based on both the AoA and theestimated range. These could be communicated both numerically andgraphically. For example, a vertical bar graph, where the bar lengthgrows with field strength could be used to communicate both fieldstrength and the rate of change of field strength. The levels at thebottom and top of the bar graph could be indicated numerically and beuser adjustable, such as by top and bottom values or span and centervalues. For another example, the various FSI metrics could also bedisplayed on a dial, or set of dials, or a multi-hand clock with asensitive (e.g. “seconds”) hand and a less sensitive (e.g. “minutes”)hand, where clockwise motion means the level is increasing,counter-clockwise motion means the level is decreasing, and each 360degree turn causes a numerical counter, or the next dial over, oranother hand, or a color index, to increment or decrement accordingly. Auser setting could allow the operator to choose how many dB changecaused a 360 degree turn, allowing high sensitivity to field strengthchanges. For example, using a clock like dial display, the operatorcould set the “seconds hand” to 2 dB per rotation, and the “minuteshand” to 60 dB per rotation allowing both fine scale and large scalechanges to be communicated nearly instantly in a way that the operatorcould remember the recent history. Assuming PF=2 (free space), every 6dB increase in the FSI means the distance to the target has been cut inhalf.

By virtue of capturing the various electromagnetic field components, thedisclosed RF emitter sensing system can computationally rotate thecardioid beam patterns produced at the antenna ports. The feature isused in Equations 43 and 44 to find the field strength of the forwardand reflected waves. Preferred embodiments would include a graphicalplot of the field strength as a function of a beam pointing angle (i.e.yin equation 43) as such a pattern would aid the operator in somemultipath environments. Most embodiments would include a graphicalcompass line showing the bearing to the emitter and the bearing to areference heading (e.g. north).

CONCLUSION

This disclosure is intended to explain how to fashion and use variousembodiments in accordance with the invention rather than to limit thetrue, intended, and fair scope and spirit thereof. The foregoingdescription is not intended to be exhaustive or to limit the inventionto the precise form disclosed. Modifications or variations are possiblein light of the above teachings. The embodiments were chosen anddescribed to provide the best illustration of the principles of theinvention and its practical application, and to enable one of ordinaryskill in the art to utilize the invention in various embodiments andwith various modifications as are suited to the particular usecontemplated. All such modifications and variations are within the scopeof the invention as determined by the appended claims, as may be amendedduring the pendency of this application for patent, and all equivalentsthereof, when interpreted in accordance with the breadth to which theyare fairly, legally, and equitably entitled. The various circuitsdescribed above can be implemented in discrete circuits or integratedcircuits, as desired by implementation.

1-30. (canceled)
 31. An RF emitter sensing device comprising an antennacircuit, an isolation element, and an estimator element configured tooutput, for one or more incoming signal-of-interest (SoI), either orboth of an estimated range to the emitter of each SoI, and estimates forone or more angles corresponding to the angle-of-arrival (AoA) of eachSoI, wherein: the antenna circuit has a plurality of ports that eachoutput an output signal containing the one or more SoI, the antennacircuit including one or more multi-port antennas, each multi-portantenna having two or more ports, each multi-port antenna beingconfigured to pick up a combination of one or more E-field signals andone or more H-field signals from each SoI, in a common volume of space,such that the one or more E-field signals and the one or more H-fieldsignals can be isolated from each other by combining the output signals;and the isolation element is configured to output one or more isolatedSoI outputs, for each respective port by receiving the output signalsfrom each output port of the antenna circuit, and isolating in eachrespective port, one or more SoI from other extraneous signals; and theestimator element is configured to output either or both of an estimatedrange to the emitter of each SoI, and estimates for one or more anglescorresponding to the AoA of each SoI by: receiving the output signalsfrom the antenna circuit, and generating either or both of an estimatedrange to the emitter of each SoI, and estimates for one or more anglescorresponding to the AoA of each SoI.
 32. The RF emitter sensing deviceof claim 31 also receiving or having access to user data that includesSoI-isolation-metrics corresponding to each SoI wherein, the isolationelement is configured to isolate the one or more SoI from otherextraneous signals according to the SoI-isolation-metrics.
 33. The RFemitter sensing device of claim 31 also receiving or having access touser data that includes SoI-isolation-metrics corresponding to each SoIwherein: the SoI-isolation-metrics include one or more of, timeintervals when the SoI is known or likely to be active, time intervalswhen the SoI is known or likely to be inactive, field strength range,center frequency, bandwidth, modulation characteristics, occurrencetiming, repetition rate, polarization, field strength range, stabilityof field strength, constraints on a range of potential angles ofarrival, and multipath geometries; and the isolation element isconfigured to isolate the one or more SoI from other extraneous signalsaccording to the SoI-isolation-metrics.
 34. The RF emitter sensingdevice of claim 31 wherein the one or more multi-port antennas include amultiport antenna that is comprised of one or moreconductive-surface-pairs, wherein, each conductive-surface-pair has afirst conductive surface, a second conductive surface offset in anoffset-direction from the first conductive surface, and one or moreport-pairs, each port-pair including a first port and a second port;wherein each of the first and second port is formed by a connection tothe first and second conductive surfaces, and wherein each of the one ormore port-pairs forms a loop going from a first terminal of acorresponding first port, through the first conductive surface to afirst terminal of a corresponding second port, through a terminationload connected across the corresponding second port to a second terminalof the corresponding second port, and through the second conductivesurface to a second terminal of the corresponding first port, andthrough a termination load connected across the corresponding firstport, back to the first terminal of the corresponding first port tocomplete the loop, and an output for each port; and differentconductive-surface-pairs have different offset-directions and the loopsassociated with the port-pairs share a nominally common center point.35. The RF emitter sensing device of claim 31, wherein the estimatorelement is configured to output either or both of an estimated range tothe emitter of an SoI, and estimates for one or more anglescorresponding to the AoA of an SoI by also: computing the estimatedrange and/or one or more angle estimates based on a computation that isa function of: the received output signals from the antenna circuit, anda set of one or more baseline values determined with one or more knownSoI, with each of the one or more known SoI at one or more knownpositions or angles.
 36. The RF emitter sensing device of claim 31,wherein the estimator means is configured to, for each SoI: isolateE-field signals from the SoI by combining output signals from theantenna circuit, and isolate H-field signals from the SoI by combiningoutput signals from the antenna circuit, and the estimator means isconfigured to output either or both of an estimated range to the emitterof the SoI, and estimates for one or more angles corresponding to theAoA of the SoI by also by using one or more of: the magnitude ofcombinations of the isolated E-field signals from the SoI and theisolated H-field signals from the SoI, and the phase of combinations ofthe isolated E-field signals from the SoI and the isolated H-fieldsignals from the SoI.
 37. The RF emitter sensing device of claim 31,wherein the antenna circuit is configured to pick up signals at a morethan one location or orientation, and the one or more locations ororientations are made with one or more of a sequential configuration anda simultaneous configuration; wherein, in the sequential configuration,ports are in respective initial locations and orientations at an initialtime, and ports are in a respective next location and orientation at anext time that is later than the initial time, and wherein the estimatoruses the output signals received at different times.
 38. The RF emittersensing device of claim 31 wherein the estimator element is configuredto output either or both of an estimated range to the emitter of an SoI,and estimates for one or more angles corresponding to the AoA of an SoIby also: computing the estimated range and/or one or more angleestimates based on a computation that is a function that uses thereceived output signals from the antenna circuit, wherein the functionis configured to mitigate estimation bias caused by one or more of:receiver noise, noise picked up by the antennas, sensitivity imbalancein the E and H fields picked up by a port, the magnitude of an SoI,effects of non-ideal termination impedances attached to the antennaports, and the effects of objects causing reflections into the antennacircuit or blockages to the antenna circuit.
 39. The RF emitter sensingdevice of claim 31, wherein the estimator element is configured togenerate, for each SoI, one or more angles corresponding to the AoA ofeach SoI, by also: computing, for each SoI, a set of measured valuesbased on the one or more isolated SoI outputs from the isolation means,comparing, for each SoI, the set of measured values with a plurality ofsets of calibration values, where the plurality of sets of calibrationvalues is comprised of sets of values determined with the SoI emitter atknown, one or more of, location, AoA, and range.
 40. The RF emittersensing device of claim 39 wherein each value set is derived from theoutputs of an i^(th) port pair and includes a first quantity A_(i) and asecond quantity B_(i), where i is an index value from 1 to N, wherein,the first quantity A_(i) is a difference between a first SoI level and asecond SoI level, the second quantity B₁ is the sum of the first SoIlevel and the second SoI level.
 41. The RF emitter sensing device ofclaim 39 wherein, a set of real-time derived values is derived from theset of measured value sets, the set of desired outputs are contained ina lookup table where each row contains the list of the desired outputsin a first set of columns, and a set of expected derived values,corresponding to the list of desired outputs, in a second set ofcolumns, and determining the list of desired outputs involves finding arow where the set of expected derived values most closely matches theset of real-time derived values, and corresponding to the row found,reading from the first set of columns the list of desired output values.42. The RF emitter sensing device of claim 39 wherein, the set ofreal-time derived values includes a plurality of ratio quantitiescorresponding to each port-pair, and each ratio quantity is the firstquantity divided by the second quantity for each of the plurality ofport-pairs.
 43. The RF emitter sensing device of claim 39 wherein, a setof real-time derived values is derived from the set of measured valuesets, the set of real-time desired outputs are contained in a lookuptable where each row contains a first set of columns including the listof desired outputs, a second set of columns including a set ofcorresponding expected derived values, and a third set of columns thatindicate, in each row, which values in the second set of columns areactive for that particular row; and determining the list of desiredoutputs involves finding the row where the set of the set of expectedderived values that are active according to the third set of columns,most closely matches the set of real-time derived values, andcorresponding to the row found, reading from the first set of columnsthe list of desired output values.
 44. The RF emitter sensing device ofclaim 39 wherein a set of derived values includes a plurality of valuepairs corresponding to a plurality of port-pairs, and for each portpair, the value pair is the arc-sine and arc-cosine of a ratio quantitywhich is the first quantity divided by the second quantity.
 45. The RFemitter sensing device of claim 39 wherein the first SoI level and thesecond SoI level are generated by: coherently estimating a first initialSoI level corresponding to the first port and a second initial SoI levelcorresponding to the second port, and correcting for any imbalance inthe E-field and H-field sensitivities embedded in the first initial SoIlevel, and the second initial SoI level to generate the first SoI leveland the second SoI level.
 46. The RF emitter sensing device of claim 45,wherein the estimator is configured such that the coherently estimatingis performed by choosing from the plurality of ports a different port,having a high SoI level relative to all the ports and that is neitherthe first port nor the second port, and finding a first initial SoIlevel that is a first correlation between the first port and thedifferent port over a time period which may be discontinuous, finding asecond initial SoI level that is a second correlation between the secondport and the different port over a time period which may bediscontinuous, and the correcting for any imbalance is performed bycomputing the sum of the first initial SoI level and the second initialSoI level, computing the difference between the initial SoI level andthe second initial SoI level, computing a value M, which is thedifference divided by the sum, having, for each said port-pair, a knownor measured back-to-front ratio, {circumflex over (ε)}, at the frequencyof the SoI, and computing a correction factor k for each port pair thatis one divided by the quantity 1 minus twice a measured back-to-frontratio {circumflex over (ε)}, (k=1/(1−2{circumflex over (ε)})) at thefrequency of the SoI, such that computing the first SoI level to beone-half of M times the quantity of 1 plus k (M(1+k)/2), and computingthe second SoI level to be one half of M times the quantity of 1 minusk, (M(1−k)/2).
 47. The RF emitter sensing device of claim 39, whereinthe antenna system includes one or more pairs of port-pairs, such as ani^(th) port-pair and a j^(th) port pair, where i and j are indexes,wherein, j is not equal to i, the patterns of the first port and thesecond port in each of the port-pairs are aimed in opposite directions,all the ports in each pair of port-pairs share the same polarizationaxis, the aiming axis of the i^(th) port-pair is orthogonally to thej^(th) port-pair, and the estimator is configured to determine the listof desired outputs by correcting for homogeneous noise ξ_(i,j) picked upby each of the ports by estimating the homogeneous noise and removingits affect.
 48. The RF emitter sensing device of claim 47, wherein theestimator module is further configured to estimate the homogeneous noiseξ_(i,j) such that,$\xi_{i,j} = {{\Phi \left( {A_{i},B_{i},A_{j},B_{j}} \right)} = {{Re}\left\lbrack {\frac{B_{i}}{2} + \frac{B_{j}}{2} - \sqrt{\frac{F}{6} + \frac{H}{4} + \frac{I}{144}} - \sqrt{\frac{F}{3} - \frac{H}{4} - \frac{I}{144} - \frac{3E}{\sqrt{I + {36H} + {24F}}}}} \right\rbrack}}$wherein A_(i), B_(i), A_(j), B_(j) are the first and second quantitiesof the i^(th) and j^(th) port-pairs respectively$\mspace{20mu} {{E = {{A_{i}^{2}B_{i}} - {A_{j}^{2}B_{i}} - {A_{i}^{2}B_{j}} + {A_{j}^{2}B_{j}}}},\mspace{20mu} {F = {A_{i}^{2} + {B_{i}^{2}/2} - {B_{i}B_{j}} + A_{j}^{2} + {B_{j}^{2}/2}}},\mspace{20mu} {G = {\left( {B_{i} - B_{j}} \right)^{2}\left( {{4A_{i}^{2}} - B_{i}^{2} + {2B_{i}B_{j}} + {4A_{j}^{2}} - B_{j}^{2}} \right)}},{H = \sqrt[\frac{1}{3}]{\begin{matrix}{{\sqrt{3\left( {{432E^{4}} - {64E^{2}F^{3}} + {G\left( {{16F^{4}} - {144E^{2}F}} \right)} + {8F^{2}G^{2}} + G^{3}} \right)}/72} +} \\{{E^{2}/2} - {F^{3}/27} + {{G\left( {{2B_{i}B_{j}} - {2A_{i}^{2}} - B_{i}^{2} - {2A_{j}^{2}} - B_{j}^{2}} \right)}/24}}\end{matrix}}},\mspace{20mu} {I = \left\{ {\begin{matrix}{\left( {{4F^{2}} - {3G}} \right)/H} & {{{if}\mspace{14mu} H} \neq 0} \\0 & {{{if}\mspace{14mu} H} = 0}\end{matrix},} \right.}}$ and the estimator is configured to estimate anangle of arrival from the (i,j) pair of port-pairs using a four quadrantarctangent function (e.g. a tan 2(y,x) Fortran function), where thearguments are A_(i)/(B_(i)−ξ_(i,j)) and A_(j)/(B_(j)−ξ_(i,j)).
 49. TheRF emitter sensing device of claim 47, wherein the estimator modulefurther: operates to estimate the homogeneous noise ξ_(i,j) for aparticular (i,j) pair of port-pairs, such that${\xi_{i,j} = {{\Phi \left( {A_{i},B_{i},A_{j},B_{j}} \right)} = {{Re}\left\lbrack {\frac{B_{i}}{2} + \frac{B_{j}}{2} - \sqrt{\frac{F}{6} + \frac{H}{4} + \frac{I}{144}} - \sqrt{\frac{F}{3} - \frac{H}{4} - \frac{I}{144} - \frac{3E}{\sqrt{I + {36H} + {24F}}}}} \right\rbrack}}},$wherein are the first and second quantities of the i^(th) and j^(th)port-pairs respectivelyE=A _(i) ² B _(i) −A _(j) ² B _(i) −A _(i) ² B _(j) +A _(j) ² B _(j),$\mspace{20mu} {{F = {A_{i}^{2} + {B_{i}^{2}/2} - {B_{i}B_{j}} + A_{j}^{2} + {B_{j}^{2}/2}}},\mspace{20mu} {G = {\left( {B_{i} - B_{j}} \right)^{2}\left( {{4A_{i}^{2}} - B_{i}^{2} + {2B_{i}B_{j}} + {4A_{j}^{2}} - B_{j}^{2}} \right)}},{H = \sqrt[\frac{1}{3}]{\begin{matrix}{{\sqrt{3\left( {{432E^{4}} - {64E^{2}F^{3}} + {G\left( {{16F^{4}} - {144E^{2}F}} \right)} + {8F^{2}G^{2}} + G^{3}} \right)}/72} +} \\{{E^{2}/2} - {F^{3}/27} + {{G\left( {{2B_{i}B_{j}} - {2A_{i}^{2}} - B_{i}^{2} - {2A_{j}^{2}} - B_{j}^{2}} \right)}/24}}\end{matrix}}},\mspace{20mu} {I = \left\{ {\begin{matrix}{\left( {{4F^{2}} - {3G}} \right)/H} & {{{if}\mspace{14mu} H} \neq 0} \\0 & {{{if}\mspace{14mu} H} = 0}\end{matrix},} \right.}}$ and operates to generate a set of derivedvalue sets for each pair of port-pairs that includes the valuesA_(i)/(B_(i)−ξ_(i,j)), and (B_(i)−ξ_(i,j))/(B_(j)−ξ_(i,j)), for each(i,j) pair of port-pairs, includes a lookup table in which each rowcontains, the angles from the list of desired outputs in a first set ofcolumns, and corresponding to these angles, the expected values for theset of derived value sets, in a second set of columns; and operates todetermine the list of desired outputs by finding the row where theexpected values most closely match the values in the set of derivedvalue sets, and reading from the first set of columns in that row, thelist of output values.
 50. An RF emitter sensing device, comprising: anantenna-system including one or more antenna elements; an isolationmeans configured to receive a signal from each port of theantenna-system, and isolate, for each port, a signal of interest (SoI)from other extraneous signals based on the SoI-isolation-metrics, andoutput, for each corresponding antenna-system port, an isolated SoIoutput; a combing module that that includes N combiners, each combinerconfigured to generate an output-pair that includes a first output and asecond output, where the first output and the second output both havepatterns that are nominally a raised sine, and aim in oppositedirections, where N is one or more, and where we will use i or j tocorrespond to and reference a particular output-pair by taking its valuefrom 1 to N, and an estimator module configured to receive the pluralityof output-pairs from the combining module, and generate the list ofdesired outputs for each SoI by using the plurality of SoI-quad-sets,and user data; and output the list of desired outputs; wherein theestimator means estimates and computes the SoI angle of arrival bycomputing a set of measured value sets, one value set for eachoutput-pair, where each value set contains a first quantity A_(i), asecond quantity B_(i), and where the first quantity A_(i) is thedifference between a first SoI level and a second SoI level, and wherethe second quantity B_(i) is the sum of the first SoI level and thesecond SoI level, and where the first SoI level and the second SoI levelare derived using the SoI received on the first port and the secondport, and determining the list of desired outputs based on a set ofdesired outputs that correspond to a set of potential value sets, andthe set of measured value sets; wherein the output-pairs are organizedinto one or more quad-sets that each include pairs of output-pairs(i,j), where both output-pairs share the same polarization but aim inorthogonal directions, such that j is never equal to i; and wherein theestimator module operates to correct for homogeneous noise ξ_(i,j)picked up by each quad-set by, estimating the homogeneous noise for aparticular (i,j) quad-set such that${\xi_{i,j} = {{\Phi \left( {A_{i},B_{i},A_{j},B_{j}} \right)} = {{Re}\left\lbrack {\frac{B_{i}}{2} + \frac{B_{j}}{2} - \sqrt{\frac{F}{6} + \frac{H}{4} + \frac{I}{144}} - \sqrt{\frac{F}{3} - \frac{H}{4} - \frac{I}{144} - \frac{3E}{\sqrt{I + {36H} + {24F}}}}} \right\rbrack}}},$wherein A_(i), B_(i), A_(j), B_(j) are the first and second quantitiesof the i^(th) and j^(th) port-pairs respectively$\mspace{20mu} {{E = {{A_{i}^{2}B_{i}} - {A_{j}^{2}B_{i}} - {A_{i}^{2}B_{j}} + {A_{j}^{2}B_{j}}}},\mspace{20mu} {F = {A_{i}^{2} + {B_{i}^{2}/2} - {B_{i}B_{j}} + A_{j}^{2} + {B_{j}^{2}/2}}},\mspace{20mu} {G = {\left( {B_{i} - B_{j}} \right)^{2}\left( {{4A_{i}^{2}} - B_{i}^{2} + {2B_{i}B_{j}} + {4A_{j}^{2}} - B_{j}^{2}} \right)}},{H = \sqrt[\frac{1}{3}]{\begin{matrix}{{\sqrt{3\left( {{432E^{4}} - {64E^{2}F^{3}} + {G\left( {{16F^{4}} - {144E^{2}F}} \right)} + {8F^{2}G^{2}} + G^{3}} \right)}/72} +} \\{{E^{2}/2} - {F^{3}/27} + {{G\left( {{2B_{i}B_{j}} - {2A_{i}^{2}} - B_{i}^{2} - {2A_{j}^{2}} - B_{j}^{2}} \right)}/24}}\end{matrix}}},\mspace{20mu} {I = \left\{ {\begin{matrix}{\left( {{4F^{2}} - {3G}} \right)/H} & {{{if}\mspace{14mu} H} \neq 0} \\0 & {{{if}\mspace{14mu} H} = 0}\end{matrix},} \right.}}$ and removing the effect of the homogeneousnoise by generating a set of derived value sets including aquad-output-value-set for each quad-set, that is comprised of a firstterm A_(i)/(B_(i)−ξ_(i,j)), a second term A_(j)/(B_(j)−ξ_(i,j)), andsometimes a third term (B_(i)−ξ_(i,j))/(B_(j)−ξ_(i,j)), for a said (i,j)quad-set, and wherein the estimator module includes a lookup table inwhich each row contains, the list of desired outputs in a first set ofcolumns, and corresponding to the values in the list, and the expectedvalues for the set of derived value sets, in a second set of columns,wherein the estimator module is configured to find the row where theexpected values most closely match the values in the set of derivedvalue sets, and read from the first set of columns in that row, the listof output values, and wherein the user data includes for each SoI,SoI-isolation-metrics that can be used to isolate the SoI, including oneor more of the center frequency, bandwidth, modulation characteristics,occurrence timing, repetition rate, polarization, field strength,stability of field strength, constraints on the range of potentialangles of arrival, and known multipath geometries; and specificationsfor a list of desired outputs for each particular SoI, including one ormore items such as the coordinate system and pose used, time and date,azimuth angle, desired azimuth angle accuracy and confidence level,achieved azimuth angle accuracy and confidence level, elevation angle,desired elevation angle accuracy and confidence level, achievedelevation angle accuracy and confidence level, maximum processing timeallowed, processing time used, time periods used to integrate SoIenergy, polarization, center frequency, modulation type, repetitionrate, peak-to-average ratio, variance, times to a number of the highestindependent peaks, frequency versus time profile, power versus timeprofile, and rms power. a configuration of the antenna system includinga position and beam pattern associated with each port in the antennasystem relative to a reference position on the DF system, where the beampattern includes one or more of magnitude, polarization, group-delay,transfer function, and impulse response as a function of angles, and thetime, date and pose of a reference position on the DF system relative toan earth coordinate system.